Accomack County Schools Curriculum Guide
First Grade Mathematics
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.1 The student will a) count from 0 to 100 and write the corresponding numerals; and b) group a collection of up to 100 objects into tens and ones and write the corresponding numeral to develop an understanding of place value.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
ESSENTIAL UNDERSTANDINGS
There are three developmental levels of counting:
– rote sequence;
– one-to-one correspondence; and
– the cardinality of numbers.
All students should
Associate oral number names with the correct numeral and set of objects.
Counting involves two separate skills: verbalizing the list of standard number words in order (“one, two, three,
”) and connecting this sequence with the items in the set being counted, using oneto-one correspondence. Association of number
Understand that 1 and 10 are special units of numbers (e.g., 10 is 10 ones, but it is also 1 ten).
Understand the ten-to-one relationship of words with collections of objects is achieved by ones and tens (10 ones equals 1 ten). moving, touching, or pointing to objects as the number words are spoken.
The last number stated represents the number of objects in the set. This is known as the cardinality
Understand that numbers are written to show how many tens and how many ones are in the number. of the set.
Rote counting is a prerequisite skill for the understanding of addition, subtraction, and the ten-to-one concept of place value.
Articulating the characteristics of each numeral when writing numbers has been found to reduce the amount of time it takes to learn to write
numerals.
Understand that groups of tens and ones can be used to tell how many.
The number system is based on a pattern of tens where each place has ten times the value of the
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Count by rote from 0 to 100, using the correct name for each numeral.
Use the correct oral counting sequence to tell how many objects are in a set.
Write numerals correctly.
Write each numeral from 0 to 100.
Read two-digit numbers when shown a numeral, a Base-10 model of the number, or a pictorial representation of the number.
Identify the place value (ones, tens) of each digit in a twodigit numeral (e.g., The place value of the 2 in the number
23 is tens. The value of the 2 in the number 23 is 20).
Group a collection of objects into sets of tens and ones.
Write the numeral that corresponds to the total number of objects in a given collection of objects that have been grouped into sets of tens and ones.
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.1 The student will a) count from 0 to 100 and write the corresponding numerals; and b) group a collection of up to 100 objects into tens and ones and write the corresponding numeral to develop an understanding of place value.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only) place to its right. This is known as the ten-to-one concept of place value.
Opportunities to experience the relationships among tens and ones through hands-on experiences with manipulatives are essential to developing the ten-to-one place value concept of our number system and to understanding the value of each digit in a two-digit number. Ten-toone trading activities with manipulatives on place value mats provide excellent experiences for developing the understanding of the places in the
Base-10 system.
Models that clearly illustrate the relationships among tens and ones are physically proportional
(e.g., the tens piece is ten times larger than the ones piece).
Providing students with opportunities to model two-digit numbers expressed with groups of ones and tens will help students understand the ideas of trading, regrouping, and equality.
Recording the numeral when using physical and pictorial models leads to an understanding that the position of each digit in a numeral determines the size of the group it represents.
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.1a Continued
Teacher Resources:
Text : SBG Mathematics 1999
Chapter – Lesson , page 6.11, p. 185-186
Test : Saxon Math Second Edition
Lesson 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19-111
Manipulatives: counters, 100 chart, numberlines
Aims (Counting): Fall Into Math and Science “Weather Wear” pgs. 22-24; “Apples A Peel To Me” pg.
25-32; “Don’t Leaf Out the Vegetables” pg. 46-48; “Spinning Ghosts” pg. 49-50; “An Eye Full of Color” pg. 5-10; “You Can Count on Us” pg. 1-4; Glide Into Winter With Math and Science “Electric Breakfast
1” pg. 29-31; “Electric Breakfast 11” pg. 32-34; “All Aboard the Chow Express” pg. 58-67; “Do You
Have A Snoot for Fruit?” pg. 58-67; Spring Into Math and Science “Floating Fruit” pg. 46-49; “Flowers” pg. 84-86; Primarily Physics “I Love Color” pg. 56-58
Aims (Writing): Glide Into Winter With Math and Science “Polar Bear Pie,” pg. 19-21; “Valentine
Candy Count,” pg. 35-41; “You Are All Heart,” pg. 42-44; Spring Into Math and Science “Animal
Crackers,” pg. 42-45; Primarily Plants “The Seed Within,” pg. 26-29; Primarily Physics “Eggs-ful of
Sound,” pg. 22-24; Primarily Bears “The Jar that Likes to Keep You Guessing,” pg. 77-82
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, http://illuminations.ntcm.org/activitydetail.aspx?id=75 , Education City
Virginia Department of Education Training Modules: Patterns, Functions, & Algebra- Section 2
Activity 4A “Grid Pictures on the Hundred Chart” ; Section 4 Activity 3 “Build the Rule”
Children’s Literature (Counting) : Ten Black Dots by Donald Crews, One Sun Rises by Wendy
Hartmann, 12 Ways to Get to 11 by Eve Merriam, When Sheep Cannot Sleep, The Counting Book by
Satashi Kitamwa, Counting Sheep by John Archambault, One Crow by James Aylesworth, Names, Sets and Numbers by Jeanne Bendick, How Many Bugs in a Box by David Carter, Fish Eyes, A Book You
Can Count On by Lois Ehlert, The Ants Go Marching by Bernice Freschet, Each Orange Had 8 Slices by
Paul Giganti Jr., Count Your Way Through the Arab World by Jim Haskins, Nina Duck Nine by Sarah
Hayes, More Than One by Tana Hoban, 1 Hunter by Pat Hutchins, 17 Kings and 42 Elephants by
Margaret Mahy, The Hundred-Penny Box by Sharon Mathis, When One Cat Woke Up by Judy Astley,
One Old Oxford Ox by Nicola Bayley, Count-A-Saurus by Nancy Blumenthal, Number Ideas through
Pictures by Mannis Charosh, Mojo Means One: the Swahili Counting Book by M. Feelings, Roll Over by
Mordicai, Gerstein, How Many Feet in the Bed? By D.J. Hamm, Count and See by Tana Hoban, Dirty
Dozen Dogs by William Hooks, Swimmy by Leo Lionni, Bunches and Bunches of Bunnies by Louise
Mathews, Five Little Monkeys Sitting in a Tree by Eileen Cristelow, How Many Snails? by Paul Giganti
Jr., Monster Math by Grace Maccarone , The Crayola Counting Book by Rozanne Lanczak Williams, The
Crayon Counting Book by Pam Munoz Ryan & Jerry Pallotta, The Icky Bug Book by Jerry Pallotta, The
Cheerios counting Book by Barbara McGrath, Let’s Count it Out Jesse Bear by Nancy White Carlstrom
Accomack County Schools Curriculum Guide
First Grade Mathematics
Children’s Literature (Writing) : Anno’s Counting Book by Mitsumasa Anno; Anno’s Counting House by Mitsumasa Anno; Bring Me What I Ask by Stacey Kaopuiki, Count on Your Fingers African Style by
Claudia Zaslavsky, How Many? From 0 to 20 by Fiona Pragoff; Hippos Go Berserk By Sandra
Boynton, Lucy and Tom’s 1,2,3 by Shirley Hughes, One Cow Moo Moo By David Bennett, One Magic
Box by Roger & Mariko Chouinard, One, Two, Buckle My Shoe by Rowan Barnes-Murphy, One, Two,
Three to the Zoo by Eric Carle, One Yellow Lion by Matthew Van Fleet, Out for the Count by Kathryn
Cave, Sea Squares by Joy N. Hulme, Ten, Nine, Eight by Molly Bang, 1 is No Fun But 20 is Plenty by
Tise-Margret Vogel, Ten Black Dots by Donald Crews, One Sun Rises by Wendy Hartman, 12 Ways to
Get 11 by Eve Merriam, Frog and Toad Are Friends by Arnold Lobel
Instructional Vignette: (Alternate Teaching Strategies) for counting to 100:
Have students make sets of manipulatives for a given amount between ten and one hundred and write the numeral representative of the amount.
Give each pair of children a paper bag and a bowl of beans. Ask the children to pass the bag and place one to five beans in the bag until a bell is rung. At that point, instruct the students to record the number of beans he/she estimates in the bag. The students then empty the contents of the bag, spilling the beans and count to see whose guess is closest to be correct.
Instruct small groups of three to four students to pass a paper or small chalkboard around the table with each student writing the next number in proper sequence until a specific number is reached.
The first group to complete the task is the winner.
Play number Bingo.
“What does 100 Look Like?” Ask partners to describe and create a set of 100.
Plan a parade and start and stop the music while students march and clap. Have the children count their claps orally as they march.
Roll and color/Roll and Write – see instructions below
Instructional Vignette: (Alternate Teaching Strategies) for writing numerals to 100.
Place shaving cream on every child's desk. Call out a number for the students to write with their finger in the cream. Write the number on the board so the students can check their work. The students need only to rub the surface of their desk to erase their work and be ready to write again.
Give students number cards to arrange in the proper order. Allow students to spread out on the
1
Accomack County Schools Curriculum Guide
First Grade Mathematics floor and work with a partner when necessary.
Have students write missing numbers on a hundreds chart.
Play “Secret Number”. Give clues for students to identify a secret number. Examples might include: “The secret number comes before 65. The secret number comes after 79.”
Begin counting, pause, and have the students count on.
Fill Ziplock baggies with finger paint or gel, etc. and seal. Have students practice forming numbers.
Additional Vocabulary:
Numeral— A symbol used to represent a number.
Standard 1.1b
Teacher Resources:
Text : SBG Mathematics 1999
Chapter / Lesson, page SBG text does not correlate with Virginia SOL 1.2
Text : Saxon Math Second Edition
Lesson 53, 84, 85
Manipulatives: counters, 100 chart, numberlines
Aims: Primarily Bears “The Jar that Keeps You Guessing”
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City
Children’s Literature : Ten Go Hopping by Viv Allbright, Two Hundred Rabbits by Lonzo Anderson and
Adrienne Adams, Ten for Dinner by Jo Ellen Bogart, Ten Black Dots by Don Crews, Two Hundred Dresses by Eleanor Estes, Millions of Cats by Wanda Gag, The 500 Hats of Bartholomew Cubbins by T.S. Geisel
(Dr. Suess), Ten Apples Up on Top by Theo Le Sing, Two Ways to Count to Ten by Dee, Too Many
Tamales by Gary Soto, One Hundred Hungry Ants by Ellinoz Princzes, 17 Kings and 42 Elephants by
Margaret Mahy, One Hundred is a Family by Pam Munoz Ryan, Cherrios Counting Book by Barbara
Barbierl, Bat Jamboree by Kathi Appalt, How Much is a Million? By David Schwartz, If You Made a
Million by David Schwartz, A Million Fish More or Less by Patricia C. McKissack, The 100 th Day of
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Accomack County Schools Curriculum Guide
First Grade Mathematics
School by Angela Shelf Medearis
Instructional Vignette: (Alternate Teaching Strategies)
Fill an Order – Separate the class into three groups, with each group having a boss.
The boss gives each worker an order, such as 99 is ___tens and ___ones. The student has to complete the order and put the correct number of unifix cubes in a baggie to fill the order. When completed, the child takes the order back to the boss. If correct, the student receives another order. If incorrect, he is referred to the teacher for help.
Use place value mats (divided into tens and ones) to group base ten pieces, unifix cubes, straws, etc.
Use Dixie cups to group beans, macaroni noodles, etc into groups of ten.
Arrange a random set of manipulatives on a desk. Give students a long piece of yarn to circle the manipulatives into sets of ten without moving the manipulatives.
Provide students with a poster sectioned off like a parking lot. Each section on the lot is filled with a number. Invite students to match cut out cars that have a number written as tens and ones to the proper number on the lot. The car with 2 tens and 9 ones should be parked in the spot 29.
Additional Vocabulary:
Place Value – the value of a place of a digit in a number
Digit – any one of these ten symbols: 1,2,3,4,5,6,7,8,9
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Accomack County Schools Curriculum Guide
First Grade Mathematics
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1 2 3 4 5 6 7 8 9 10
100
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
The patterns developed as a result of skip counting are precursors for recognizing numeric patterns, functional relationships, and concepts underlying money, time telling, and multiplication. Powerful models for developing these concepts include counters, number line, hundred chart, and calculators.
Skip counting by twos supports the development of the concept of even numbers.
Skip counting by fives lays the foundation for reading a clock effectively and telling time to the nearest five minutes, counting money, and developing the multiplication facts for five.
Skip counting by tens is a precursor for use of place value, addition, counting money, and multiplying by multiples of 10.
Counting backward by rote lays the foundation for subtraction. Students should count backward beginning with 30, 29, 28, … through …3, 2, 1, 0.
Calculators can be used to reinforce skip counting.
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
All students should The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Understand that collections of objects can be grouped and skip counting can be used to count the collection.
Understand that collections of objects can be grouped and skip counting can be used to count the collection.
Describe patterns in counting by ones (both forward and backward) and skip counting and use those patterns to predict the next number in the counting sequence.
Describe patterns in counting by ones (both forward and backward) and skip counting and use those patterns to predict the next number in the counting sequence.
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.2 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter /Lesson, page 6.12, p. 187-188, SBG text does not correlate with Virginia SOL 1.3Se
Text : Saxon Math Second Edition
Lesson 34, 46, 47, 54, 70, 90, 98
Manipulatives: counters, 100 chart, calculators, number lines, cubes, pennies, nickels, dimes
Aims: Glide Into Winter “You Are All Heart” Mathematics Their Way: “Two-Handed-Take-Away,” p.346; “Eyes”, p. 328-329; “Stars,” p. 330
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City
Children’s Literature : All My Shoes Comes In Twos by Mary Ann Hoberman, How Many Twos? By
Judy Hindley, One, Two, One Pour By Bruce McMillan, Two Ways to Count to Ten by Rudy Dee, What
Comes in 2’s, 3’s, & 4’s by Suzanne Aker, Reese’s Pieces Counting by 5’s by Jerry Pallotta and Rob
Bolster, Artic Fives Arrive by Elinor Pinczes
Virginia Department of Education Training Modules: Patterns, Functions, & Algebra—Section 2
Activity 4c “Patterning on the Hundred Chart”
Allow students to work with a partner to explore skip counting with manipulatives. Each team should make sets of 2s, 5s, and 10s. Give students large sentence strips to write the numbers for skip counting by 2s, 5s, and 10s.
Give each child a hundred chart and ask them to color numerals that represent number patterns when counting by two, fives, and tens.
Have students draw pairs of anything and write the counting pattern by 2s underneath. Examples might include socks, mittens, shoes, eyes, and hands.
Group students in a circle with one child in the middle. The student in the middle tosses a ball to different students as the class counts by 2’s, 5’s, and 10’s to 100.
Have students give each other high- fives with one hand to skip count by fives. Then students can use both hands to skip count by tens.
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Additional Vocabulary:
Multiples
Correspondence
Skip counting—A set of numbers arranged in a specific order or pattern.
Released Test Items:
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1.3 The student will identify the parts of a set and/or region that represent fractions for halves, thirds, and fourths and write the fractions.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
A fraction is a way of representing part of a whole set or a whole region.
In a set fraction model, students need opportunities to make fair shares. For example, when sharing a set of 12 markers with three friends, each person would have one-third of the whole set. Also, each element of the set, no matter its size, is considered to be an equal share of the whole.
In a region/area fraction model, a whole is broken into equal-size parts and reassembled into one whole.
The words denominator and numerator are not required at this grade, but the concepts of part and whole are required for understanding of a fraction.
At this level, students are expected to first understand the part-whole relationship (e.g., three out of four equal parts) before being expected to recognize or use symbolic representations for fractions (e.g., Ошибка!
, Ошибка!
, or
Ошибка!
).
Students should have opportunities to make connections and comparisons among fraction representations by connecting concrete or pictorial representations with spoken representations (e.g., “one-half,” “one out of two
ESSENTIAL UNDERSTANDINGS
All students should
Understand that a fraction represents a part of a whole.
Understand that fractional parts are equal shares of a whole.
Understand that the fraction name ( half , third , fourth ) tells the number of equal parts in the whole.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Represent a whole to show it having two equal parts and
1 2 identify one-half ( ), and two halves ( ).
2 2
Represent a whole to show it having three equal parts and identify one-third (
1
3
), two-thirds (
2
3
) and three-thirds (
3
3
).
Represent a whole to show it having four equal parts and
1 2 identify one-fourth ( ), two-fourths ( ), three-fourths (
4 4
3 4
) and four-fourths ( ).
4 4
Identify and model halves, thirds, and fourths of a whole, using the set model (e.g., connecting cubes and counters), and region/area models (e.g., pie pieces, pattern blocks, geoboards, paper folding, and drawings).
Name and write fractions represented by drawings or concrete materials for halves, thirds, and fourths.
Represent a given fraction using concrete materials, pictures, and symbols for halves, thirds, and fourths. For example, write the symbol for one-fourth, and represent it with concrete materials and pictures.
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1.3 The student will identify the parts of a set and/or region that represent fractions for halves, thirds, and fourths and write the fractions.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only) equal parts, ”or “two-thirds,” “two out of three equal parts,” and “one half is more than one fourth of the same whole”).
Informal, integrated experiences with fractions at this level will help students develop a foundation for deeper learning at later grades. Understanding the language of fractions (e.g., thirds means
“three equal parts of a whole”) furthers this development.
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.3 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 5.10 p. 147-148; 5.11 p. 149-150; 5.12 p. 151-152; 5.13 . 153-154; 5.14 p. 155-156;
5.15 p 157-158
Text : Saxon Math Second Edition
Manipulatives : pie pieces, pattern blocks, geo boards, paper foldables, drawings, counters, unifix cubes
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : Eating Fractions; Fraction Action by L. Leedy, Hershey’s Milk
Chocolate Candy Bar Fractions Book by Jerry Pallota,
Make a pizza – Give each child a paper plate. Have them color it to make it look like a pizza. Have them cut their pizza into halves, thirds or fourths and write the unit fraction on each piece.
Apple Fractions – see the Enhanced Scope and Sequence
Ben Franklin’s Kite – see the Enhances Scope and Sequence
Folding Fractions- Practice folding paper into each of the fractions, write the unit fraction on each piece.
Spill the Chips – give each child a bag with two sided colored chips. Spill the chips and practice identifying the fractional part of the set.
Fraction War- students will play in partners and will need unit cards, 1/2., 1/3 and 1/4.
At the same time each student will lay down a card and the student who has the biggest fraction wins the cards. If the students flip the same fraction, they will lay down another card until one student wins. The student who wins all the cards wins.
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Additional Vocabulary:
Fraction - A way to describe a part of a whole or a part of a group by using equal parts.
Set
Whole
Unit Fraction
Half, Third, Fourth
Fractional Parts
Region
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1.4 The student, given a familiar problem situation involving magnitude, will a) select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a threedigit numeral (e.g., 5, 50, 500); and b) explain the reasonableness of the choice.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Magnitude refers to the size of a set.
Exploring ways to estimate the number of objects in a set, based on appearance, (e.g., clustering, grouping, comparing) enhances the development of number sense.
To estimate means to find a number that is close to the exact amount. When asking for an estimate, teachers might ask, “ about how much?” or “ about how many?” or “Is this about 10 or about 50?”
Students should be provided opportunities to estimate a quantity, given a benchmark of 10 and/or 100 objects.
ESSENTIAL UNDERSTANDINGS
All students should
Develop an understanding of the order of magnitude (size) of whole numbers and use this knowledge to estimate quantities.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Select a reasonable order of magnitude for a given set from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, and 500 jelly beans in jars) in a familiar problem situation.
Given a familiar problem situation involving magnitude, explain why a particular estimate was chosen as the most reasonable from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral.
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.4 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter – Lesson, page 6.2, p. 168, 6.4, p. 172, 6.5, p. 174
E6-6
Text : Saxon Math Second Edition
Lesson Lessons in text did not correlate with Virginia Standard of Learning 1.7
Manipulatives: Guessing jars, jelly beans, rice, pictures
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : The 500 Hats of Bartholomew Cubbins by Dr. Seuss, How Much is a Million? by
David Schwartz, Millions of Cats by Wanda Gag, Counting on Frank by Rod Clement, Betcha by Stuart
Murphy, Jellybean Contest by Kathy Darling
Instructional Vignette: (Alternate Teaching Strategies)
Show the students a box of 64 crayons. Ask them to predict whether it has 6, 60, or 600 crayons. Next show them a package of cookies and ask if it has 3, 30, or 300 cookies inside. Actually count each set of objects and discuss which estimate was closest to the actual number of items.
Using a guessing jar, place objects in the jar and ask each student to estimate how many are in the jar.
Chart the response and then count how many are in the jar. Compare their responses and ask the children to explain how or why they estimated as they did.
Let children take turns collecting sets of items and having other children guess how many are in the set. Have the child give choices to the child guessing from a one-digit number, a two-digit number, and a three-digit number.
Additional Vocabulary: magnitude - Comparative size. estimate - Guess how many. reasonable set numeral quantities
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Accomack County Schools Curriculum Guide
First Grade Mathematics
1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use Only)
Associate the terms addition , adding , and sum with the concept of joining or combining.
Associate the terms subtraction , subtracting , minus , and difference with the process of taking away or separating (i.e., removing a set of objects from the given set of objects, finding the difference between two numbers, or comparing two numbers).
Provide practice in the use and selection of strategies. Encourage students to develop efficient strategies. Examples of strategies for developing the basic addition and subtraction facts include
counting back;
“one-more-than,” “two-more-than” facts;
“one-less-than,” “two-less-than” facts;
“doubles” to recall addition facts (e.g., 2 + 2 =__; o 3 + 3 =__);
“near doubles” [e.g., 3 + 4 = (3 + 3) + 1 = __];
“make-ten” facts (e.g., at least one addend of 8 or
9);
“think addition for subtraction” (e.g., for 9 – 5 =
__, think “5 and what number makes 9?”);
use of the commutative property, without naming the property (e.g., 4 +3 is the same as 3 + 4);
use of related facts (e.g., 4 + 3 = 7 , 3 + 4 = 7, 7 – 4
= 3, and 7 – 3 = 4);
use of the additive identity property (e.g., 4 + 0 =
4), without naming the property but saying, “When you add zero to a number, you always get the
ESSENTIAL UNDERSTANDINGS
All students should
Develop an understanding of the addition and subtraction relationship.
Develop addition and subtraction strategies for fact recall.
Develop fluency with basic number combinations for addition and subtraction.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Identify + as a symbol for addition, – as a symbol for subtraction, and = as a symbol for equality.
Recall and state orally the basic addition facts for sums with two addends to 18 or less and the corresponding subtraction facts.
Recall and write the basic addition facts for sums to 18 or less and the corresponding subtraction facts, when addition or subtraction problems are presented in either horizontal or vertical written format.
16
Accomack County Schools Curriculum Guide
First Grade Mathematics original number.”; and
use patterns to make sums (e.g., 0 + 5 = 5, o 1 + 4 = 5, 2 + 3 = 5, etc.).
Manipulatives should be used to develop an understanding of addition and subtraction facts.
Automaticity of facts can be achieved through constant practice which may include games, handson activities, flash cards, and paper and pencil.
Students should first master facts to 10 and then master facts to 18.
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Accomack County Schools Curriculum Guide
First Grade Mathematics
SOL 1.5 Continued:
Teacher Resources:
Text: SBG Mathematics 1999
Big Books: The Bug Book, Miss Terry’s Toy Store, Behind the Door
Chapter / Lesson , page 2.1, p. 37-38, 2.2, p. 39-40, 2.3, p. 41-42, 2.4, p. 43-44, 2.5, p. 45-46, 2.6, p. 47-
48, 2.7, p. 49-50, 2.10, p. 55-56, 2.11, p. 57-58, 2.12, p. 61-62, 63-65, 3.2, p. 69-70, 3.3, p. 71-72, 3.4, p. 73-
74, 3.5, p. 75-76, 3.6, p. 77-78, 3.7, p. 79-80, 3.8, p. 81-82, 3.9, p. 83-84, 3.10, p. 85-86, 3.11, p. 87-91, 8.1, p. 227-228, 8.2, p.229-230; 8.3, p. 231-232, 8.4, p. 233-234, 8.5, p. 235-236; 8.7, p. 239-240; 8.8, p. 241-
242; 247; 4.1, p. 97-98; 4.2 p. 99-100; 4.3 p. 101-102; 4.4 p. 103-104; 4.5 p. 105-106; 4.6 p. 107-108; 4.8 p.
111-112; 4.9, p. 113-114; 4.10, p. 115-116; 4.11, p. 117-118; 4.12, p. 119-120; 123-125
Text: Saxon Math Second Edition
Lesson 30, 32, 34, 36, 37, 41, 44, 45, 49, 58, 59, 61, 68, 69
Aims: Glide Into Math and Science “Electric Breakfast,” pg. 29-31; “Do You Have A Snoot For Fruit?” pg.
58-67; Spring Into Math and Science “Floating Fruit,” pg. 46-49; “What do You Think Will Float?,” pg. 50-
52; Critters “Fishful Thinking,” pg. 89-90; “Under Cover,” pg. 100-104; Primarily Bears “Gummy Bears,” pg. 59-64; “M & M Math,” pg. 65-68
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
, Renaissance Place
Children’s Literature : Zin! Zin! Zin! A Violin by Lloyd Moss, Ten Flashing Fireflies by Philemon Stung,
Over in the Meadow by Ezra J. Keats, A Cake for Barney by Joyce Dunbar, Addition Annie by David
Gisler, All of Our Noses Are Here by Alvin Schwartz, Annie’s Pet by Barbara Brenner, Five Little Monkeys
Jumping on the Bed by Eileen Christelow, Let’s Find Out About Addition by David Whiney, Mouse Count by Ellen Stoll Walsh, Mission Addition by Loreen Leedy, Hey Get Our Train by John Burningham,
Anansi the Spider by Gerald McDermott, Where Jamaica Go? By Dale Gottlieb Domino Addition by
Lynette Long
Virginia Department of Education Training Modules: Patterns, Functions and Algebra—Section 3,
Activity 4 “Open Sentences,” ; Section 4, Activity 2 “Fun with Function Machines”
18
Accomack County Schools Curriculum Guide
First Grade Mathematics
Instructional Vignette: (Alternate Teaching Strategies)
Demonstrate to children how to use a number line to add and subtract. Explain that to add, count ahead. To subtract, count back.
Use number cards to practice quick recall of addition/subtraction facts.
More or Less Game – Give each child a game board, ten sided dice, spinner and chips.
Each child rolls the dice, then spins the spinner. Depending on that they spin, they either put a chip on a number that is more, less, one more, one less, etc. You will have to create the spinner to your specifications.
Take Ten! – Give each student a bag with 9 red and 9 blue unifix cubs. Each child pulls out a handful and links them together. They then write the addition sentence that is made with the cubes they pulled out. They then write a corresponding subtraction fact. This game can also be played with two colored bean counters.
Fact Family House – see Enhanced Scope and Sequence (you could also do this activity with flowers)
Pyramid Ten – This game is from “Partner Games” , which is part of the Everyday
Calendar Math (Great Source) kit.
Counters In A Cup – Students play this game with a partner. Give each student a cup with some counters in it. One person takes the cup and the other person has a sheet of paper. The student with the cup hides some of the counters under the cup and leaves some out. The other student fills in a chart like the one below. The object is to work on missing addends by having the student figure out how many counters are hidden under the cup.
In
12
Out
Addition Connect 4 – See below for game board and instructions
Additional Vocabulary:
Addition
Addends
Plus
Sum
Subtraction
Different
Minus
Equality
Horizontal vertical
19
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.6 The student will create and solve one-step story and picture problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
The problem solving process is enhanced when students
– create their own story problems; and
– model word problems, using manipulatives, representations, or number sentences/equations.
Students should experience a variety of problem types related to addition and subtraction, including
– join and separate problems (action involved); join (for example: Sam had 8 pennies. Tom gave him 3 more. How many pennies does Sam have now? separate (for example: Sam had 11 pennies. He gave 3 to Tom. How many pennies does Sam have now?)
– part-part-whole problems (no action involved); missing part (for example:
There are 8 marbles. Five are shown.
How many are missing?)
– classification problems (for example:
Jane had 12 hats. Only 3 of the hats are blue. How many are not blue?)
– comparison problems (for example: Bill is 7 years old. Alice is 4 years old. How much younger is Alice than Bill?).
ESSENTIAL UNDERSTANDINGS
All students should
Understand various meanings of addition and subtraction in a variety of situations.
Understand that creating and solving problems involves the use of addition and/or subtraction.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Interpret and solve oral or written story and picture problems involving one-step solutions, using basic addition and subtraction facts (sums to18 or less and the corresponding subtraction facts).
Identify a correct number sentence to solve an oral or written story and picture problem, selecting from among basic addition and subtraction facts.
20
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.6 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 2.9, p. 53-54, 3.9, p. 83-85, Extension, p. 93, 2.12, p. 59-60; 3.1 p. 67-68; 4.7 p.
109-110; 4.13 p. 121-122; 8.9 p. 243-244
Test : Saxon Math Second Edition
Lesson 12, 15, 25, 33
Manipulatives: See SOL 1.5
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
, Renaissance Place
Children’s Literature : Frog and Toad Are Friends by Lobel, One Gorilla by Morozimi, Rooster’s Off to
See the World by Eric Carle, The Day Jimmy’s Boa Ate the Wash by Trinka Hakes Noble, Maebella’s
Suitcase by Tricia Tusa, Where Jamaica Go? By Dale Gottlieb, Five Little Monkeys Sitting in a Tree by
Eileen Christelow, Knots on a Counting Rope by Martin & Archambault
Virginia Department of Education Training Modules: Patterns, Functions & Algebra—Section 4,
Activity 3 “Build the Rule”
Instructional Vignette: (Alternate Teaching Strategies)
Ask students to select a stated number of counters out of a bag and write an addition or subtraction story problem for that number of counters in their Math journal. Exchange problems for a partner to solve.
Invite each child to select a card containing an addition statement. Direct the children to look for magazine pictures that represent countable objects that correspond to the addition statement that they have chosen. Ask the children to glue these objects onto paper. When this is completed encourage the children to trade their picture with a partner. The partner will write the number sentence that corresponds to the picture.
Act out an addition story problem.
With each activity, have students prove their answer and check for understanding through this.
Additional Vocabulary:
Solution—The answer to a problem, sometimes including the method used to solve it.
Number Sentences
Solution
21
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.7 The student will a) identify the number of pennies equivalent to a nickel, a dime, and a quarter; and b) determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Many experiences with coins help students develop an understanding of money, such as
– drawing pennies to show the value of a given coin (e.g., a nickel, a dime, or a quarter);
– playing store and purchasing classroom objects, using play money (pennies);
– representing the value of a nickel, a dime, and a quarter, using pennies; and
– trading the equivalent value of pennies for a nickel, a dime, and a quarter, using play money.
Counting money help students gain an awareness of consumer skills and the use of money in everyday life.
A variety of classroom experiences in which students manipulate physical models of money and count forward to determine the value of a collection of coins are important activities to ensure competence with counting money.
Establishing a one-to-one correspondence between the number names and the items in a set of coins (pennies, nickels, or dimes) is essential for an accurate count.
The last number stated represents the value of a collection of coins being counted. This is known as the cardinality of the set.
ESSENTIAL UNDERSTANDINGS
All students should
Develop an understanding of exchanging the appropriate number of pennies for a nickel, a dime, or a quarter.
Develop an understanding of place value by skip counting a collection of coins by ones, fives, and tens.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Identify the value of a nickel, a dime, and a quarter in terms of pennies.
Recognize the characteristics of pennies, nickels, and dimes (e.g., color, size).
Count by ones to determine the value of a collection of pennies whose total value is 100 cents or less.
Count by fives to determine the value of a collection of nickels whose total value is 100 cents or less.
Count by tens to determine the value of a collection of dimes whose total value is 100 cents or less.
Count by ones, fives, and tens to determine the value of a collection of pennies and nickels, pennies and dimes, and nickels and dimes whose total value is 100 cents or less.
Count by ones, fives, and tens to determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.
22
Accomack County Schools Curriculum Guide
First Grade Mathematics
SOL 1.7 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Big Books - Silly Sam
Chapter / Lesson, page 7.1, p. 199-200, 7.2, p. 201-202, 7.3, p. 203-204, 7.4, p. 205-206, 7.5, p. 207-208,
7.6, p. 209-210, 7.7, p. 211-212, 7.8, p. 213-214, 7.9, p. 215-216, 7.10, p. 217-218, p. 221-223
Manipulatives: coins, cash register, objects to “buy”
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
, Renaissance Place
Children’s Literature : A Chair for My Mother by Vera Williams, Alexander, Who Used to be Rich Last
Sunday by Judith Viorst, Arthur’s Funny Money by Lillian Hoban, Don’t Count Your Chicks by Parin D’
Aulair, Ingri and Edgar, Parin D’Aulair, If You Made a Million by David Schwartz, Money (An
Eyewittness Book) by Joe Gibb, The Go –Around Dollar by Barbara Adams Johnson, The Hundred Penny
Box by Sharon Mathis, The Kids’ Money Book by Neal Godfrey, The Purse by Kathy Cople, Trouble With
Money by Stan and Jan Berenstein, $1.00 Word Riddle Book by Marilyn Burns, 26 Letters and 99 Cents by
Tana Hoban, Paddy’s Pay Day by Alexandria Day, Sheep in a Shop by Nancy Shaw, The Day the Gang Got
Rich by William Kotzwinkle, Benny’s Pennies by Pat Brisson, Jelly Beans for Sale by Bruce McMillan,
Yard Sale by James Stevenson, Pigs will be Pigs by Amy Axelrod
Instructional Vignette: (Alternate Teaching Strategies)
Ask children to draw a picture of something they would like to purchase and label the object with a price.
Direct the child's partner to “pay” for the object with monies from a bank of pennies, nickels, or dimes.
Invite children to grab a handful of coins and separate the money into piles by coins. Direct the students to count the coins and record the total amount of money for each pile on paper.
Encourage children to draw coins, count the amounts and label the totals next to the drawings.
Additional Vocabulary:
Value
23
1.8
Accomack County Schools Curriculum Guide
First Grade Mathematics
The student will tell time to the half-hour, using analog and digital clocks.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Many experiences using clocks help students develop an understanding of the telling of time to the half-hour, including
– identifying the parts of an analog clock
(minute and hour hands);
– demonstrating a given time to the half-hour, using a model clock;
– writing correct digital time to the half-hour; and
– relating time on the half-hour to daily routines and school schedules (e.g., the times of TV programs, bedtime, resource time, lunch time, recess time).
ESSENTIAL UNDERSTANDINGS
All students should
Understand how to tell time to the half-hour, using an analog and digital clock.
Understand the concepts of a.m., p.m., minutes, and hours.
Understand that there are sixty minutes in an hour.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Tell time shown on an analog clock to the half-hour.
Tell time shown on a digital clock to the half-hour.
Match a written time to the time shown on a digital and analog clock to the half-hour.
24
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.8 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 9.6, p. 261-262, 9.7, p. 263-264, 9.9, p. 267-268
Text: Saxon Math Second Edition
Lesson 48, 57, 87
Aims: Primarily Bears, “Melt an Ice Cube”; Glide Into Winter, “Polar Bear Pie”
Manipluatives: clocks (digital and analog)
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
, Renaissance Place
Children’s Literature : Do You Know What Time It Is? by Roz Abisch, Teddy on Time by Pellowski, The
Boy Who Was Always Late by John Burningham, The Grouchy Ladybug by Eric Carle, Time for School,
Nathan by Lulu Delacre, What Time is it, Jeanne-Marie? by Francoise, Brendan’s Best-Timed Birthday by
Debra Gould, The Guy Who Was Five Minutes Late by Bill Grossman, Clocks and More Clocks by Pat
Hutchins, The Man Who Tried To Save Time by Phyllis Krasilovsky, Around the Clock with Harriet by
Betsy Maestro, Mr. Cuckoo’s Clock Shop by Arnold Shapiro, How I Spent My Summer Vacation by Mark
Teague, Imogene’s Antlers by David Small, Morning, Noon, and Nigh: Poems to Fill Your Day by Sharon
Taberski, Tuesday by David Weisner
Instructional Vignette: (Alternate Teaching Strategies)
Use a large clock to model set times. Direct children to make that same time on their individual clocks. Ask for volunteers to tell the time. Explain that the person called upon with the correct answer is allowed to choose the next time for everyone to make on their clock.
Set an alarm clock to ring during the day at each half-hour. When the alarm rings, have children stop what they are doing and tell the time. Record the time and the activity the students are working on at that moment.
Have students select five of their favorite TV programs. Use the Saturday paper to find the times that the programs are shown. Ask the students to show starting and ending times of their programs on their individual clocks.
Have children write a story about their favorite time of day and why in their journal.
Additional Vocabulary:
Half hour— 30 minutes.
Half past— 30 minutes after the hour.
Analog
Digital
25
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.9 The student will use nonstandard units to measure length, weight/mass, and volume.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
The process of measurement involves selecting a unit of measure, comparing the unit to the object to be measured, counting the number of times the unit is used to measure the object, and arriving at an approximate total number of units.
Premature use of instruments or formulas leaves children without the understanding necessary for solving measurement problems.
When children’s initial explorations of length, weight/mass, and volume involve the use of nonstandard units, they develop some understanding about the need for standard measurement units for length, weight/mass, and volume especially when they communicate about these measures.
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
All students should
Understand that measurement involves comparing an attribute of an object to the same attribute of the unit of measurement (e.g., the length of a cube measures the length of a book.
The weight/mass of the cube measures the weight/mass of the book. The volume of the cube measures the volume of a book).
Understand how to measure length, weight/mass, and volume using various nonstandard units of measurement.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Measure the length of objects, using various nonstandard units (e.g., connecting cubes, paper clips, erasers).
Measure the weight/mass of objects, using a balance scale with various nonstandard units (e.g., paper clips, bean bags, cubes).
Measure the volume of objects, using various nonstandard units (e.g., connecting cubes, blocks, rice, water).
26
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.9 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 10.2, p. 283-284
Text: Saxon Math Second Edition
Lesson 35
Aims: Fall Into Math and Science “How Tall Are You?” pg. 11-17; “A Weight We Go” pg. 18-21; “Fall
Leafs Me Happy” pg. 37-41; Glide Into Winter With Math and Science “How Does Your Corn Pop?” pg. 5-
10; “Whoa-That’s Heavy” pg. 71-71; Spring Into Math and Science “Feet Findings” pg. 38-41; Primarily
Plants “Inside A Seed” pg. 2-4; “It’s in the Bag” pg. 13-25; “Observing Bulbs” pg. 35-39; Bats Incredible
“Spread Your Wings”
Manipulatives: connecting cubes, blocks, water, rice, balance scales, different sized containers
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
, Renaissance Place
Children’s Literature : Bigger and Smaller by Robert Froman, How Big is a Foot? by Rolf Myller, Inch by
Inch by Leo Lionni, Is It Larger? Is It Smaller? by Tana Hoban, Long, Short, High, Low, Thin, Wide by
James Fey, Measurement: Fun, Facts, and Activities by Caroline Arnold, Reading the Numbers, and Sizes
Encountered in Everyday Life by Mary Blocksma, Ten Beads Tall by Pam Adams, The Inch Boy by Junko
Morimoto, Blue Sea by Robert Kalan.
Instructional Vignette: (Alternate Teaching Strategies)
Help children form a chain of five paper clips. Ask children to determine whether an object looks longer than the length of the paper clip chain and estimate how many clips longer the object is. Have children use paper clips to measure the object and then record their measurements as “about -paper clips long.” Ask children which object was the shortest and which was the longest.
Use manipulatives to demonstrate weight equivalencies on a balance scales.
How many crayons will it take to equal a chalkboard eraser?
Invite children to use string to measure various objects in the classroom and compare the lengths.
Have children estimate and then weigh various objects in the classroom.
Additional Vocabulary:
Length - The distance along a line or figure from one point to another.
Measure - A comparison to some other known unit, or to find the measure of something.
Nonstandard units - Units other than customary or metric units used for measurement.
Weight - A measure of how heavy an object is.
Mass
27
Volume
Length
Measure
Weight
Non-standard units
Balance scale
Released Test Items:
Accomack County Schools Curriculum Guide
First Grade Mathematics
28
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.10 The student will compare, using the concepts of more, less, and equivalent, a) the volumes of two given containers; and b) the weight/mass of two objects, using a balance scale .
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Estimation is a commonly used strategy to compare the volumes of two containers.
Determining the volume of a container by counting the number of nonstandard units (e.g., a spoonful, or scoopful of concrete material, such as jelly beans, sand, water, or rice) that can be held by the container is a precursor to comparing volumes.
A variety of activities that focus on directly comparing the volume of objects leads to an understanding of volume.
The level of difficulty in measuring volume can be increased by varying and mixing the sizes of the containers (e.g., using short, wide containers as well as tall, narrow containers).
Weight and mass are different. Mass is the amount of matter in an object. Weight is determined by the pull of gravity on the mass of an object.
The mass of an object remains the same regardless of its location. The weight of an object changes dependent on the gravitational pull at its location. In everyday life, most people are actually interested in determining an object’s mass, although they use
ESSENTIAL UNDERSTANDINGS
All students should
Understand how to fill containers with objects to determine their volume and compare the volumes of two containers.
Understand that a balance scale can be used to compare the weights of two objects using the terms more, less, or equivalent.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Compare the volumes of two containers to determine if the volume of one is more, less, or equivalent to the other, using nonstandard units of measure (e.g., a spoonful or scoopful).
Compare the volumes of two containers to determine if the volume of one is more, less, or equivalent to the other by pouring the contents of one container into the other.
Compare the weight/mass of two objects, using the terms lighter, heavier , or the same , using a balance scale. The pan containing less weight/mass will rise and the pan containing more weight/mass will fall. If the objects are of equivalent weight/mass, the two pans will balance.
29
the term weight (e.g., “How much does it weigh?” versus “What is its mass?”).
Balance scales are instruments used for comparing weight/mass. A balance scale usually has a beam that is supported in the center. On each side of the beam are two identical trays. When the trays hold equal weights, the beam is level, and the scale is
“balanced.”
Physically measuring the weights of objects, using a balance scale, helps students develop an intuitive idea of what it means to say something is “lighter,” “heavier,” or “the same.”
Experience estimating the weights of two objects (one in each hand) using the terms lighter, heavier, or the same promotes an understanding of the concept of balance.
Accomack County Schools Curriculum Guide
First Grade Mathematics
30
SOL 1.10a Continued
Accomack County Schools Curriculum Guide
First Grade Mathematics
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 10.8, p. 295-296
Text: Saxon Math Second Edition
Manipulatives: balance scale, containers, jelly beans, sand, water, rice
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Instructional Vignette: (Alternate Teaching Strategies)
Give the children a small container and cup measure. Have them use water, sand, rice, or unpopped popcorn to determine whether the container holds less than, more than, or about the same as one cup.
Experiment with various sizes and shapes of containers to determine which two hold about the same amount of beans/sand. Ask students to predict which two containers will hold about the same amount before they begin.
Direct children to observe five containers, choosing one to be the standard. Using the standard container, ask students to fill the other containers with sand, salt, water, flour, rice, or popcorn.
Discuss which containers hold more or less than the selected standard container.
Give students three to four different size containers and ask them to predict which container will hold the most and which container will hold the least. Encourage children to check their predictions by filling each container with the same “scoop” for measure. Remind the children that all containers should be filled with the same item when testing for predictions.
Additional Vocabulary:
Estimate - A number close to an exact amount, an estimate tells about how much or about how many.
Volume - The number of cubic units of space a solid figure takes up.
Mass
Weight
Estimation
Equivalent
Lighter heavier
31
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.10b Continued
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 10.5, p. 289-290, 10.6, p. 291-292, 10.7, p. 293-294
Text: Saxon Math Second Edition
Lesson 29
Manipulatives: See SOL 1.10a
Aims: Primarily Bears, Book 1 “Teddy Bears and Oranges”; Glide Into Winter “Whoa-That’s Heavy”
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Instructional Vignette: (Alternate Teaching Strategies)
Have each child demonstrate balancing two objects on a balance scale.
Ask each child to verbalize: The__weighs more than the___.
Collect an assortment of classroom objects and ask children to compare their weights using a balance scale. Estimate the weights of the objects and then weigh the actual object.
Journal writing—Encourage children to draw a balance scale to show the comparison of weight of two objects. Ask the children to label each object and write a sentence about it.
Invite the children to make critters out of their lunch milk cartons using scraps of art supplies.
Weigh the critters to see which one is the heaviest
Additional Vocabulary:
Balance scale— A tool used for comparing the mass or weight of objects.
32
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.11 The student will use calendar language appropriately (e.g., names of the months, today, yesterday, next week, last week).
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
ESSENTIAL UNDERSTANDINGS
Practical situations are appropriate to develop a sense of the interval of time between events (e.g.,
Boy Scout meetings occur every week on
Monday: there is a week between meetings).
The calendar is a way to represent units of time
(e.g., days, weeks, and months).
All students should
Understand how to use a calendar as a way to measure time.
Using a calendar develops the concept of day as a
24-hour period rather than a period of time from sunrise to sunset.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Read a calendar to locate a given day or date.
Identify the months of the year.
Identify the seven days in a week.
Determine the days/dates before and after a given day/date
(e.g., yesterday, today, tomorrow).
Determine the date that is a specific number of days or weeks in the past or in the future from a given date, using a calendar.
Identify specific dates (e.g., the third Monday in a given month).
33
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.11 Continued
Teacher Resources:
Text: SBG Mathematics 1999
Pgs. 265, 266, P9-8, R9-8, E9-8
Manipulatives: calendar, months, days of the week, monthly calendars
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature: Cookie’s Week by Cindy Ward, The Very Hungry Caterpillar by Eric Carle,
Today Is Monday by Eric Carle, Chicken Soup With Rice by Maurice Sendak, Someday Is Not A Day
Of The Week by Denise Brennan-Nelson
Instructional Vignette: (Alternate Teaching Strategies)
This SOL should be integrated into your daily Math Meeting time. Remember to look at the Essential Knowledge for the specific skills the students should master.
It’s A Date – Take an old calendar, cut it apart and laminate it. Give each child a calendar. Have them investigate the calendar and answer questions about it. (It’s A
Date and It’s A Date Book)
Additional Vocabulary:
Calendar
Today
Yesterday
Next week
Last week
Represents
Units of time
34
1.12
Accomack County Schools Curriculum Guide
First Grade Mathematics
The student will identify and trace, describe, and sort plane geometric figures (triangle, square, rectangle, and circle) according to number of sides, vertices, and right angles.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
A plane geometric figure is any twodimensional closed figure. Circles and polygons are examples of plane geometric figures.
The van Hiele theory of geometric understanding describes how students learn geometry and provides a framework for structuring student experiences that should lead to conceptual growth and understanding.
– Level 0: Pre-recognition.
Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided polygons.
– Level 1: Visualization.
Geometric figures are recognized as entities, without any awareness of parts of figures or relationships between components of a figure. Students should recognize and name figures and distinguish a given figure from others that look somewhat the same (e.g., “I know it’s a rectangle because it looks like a door, and I know that a door is a rectangle”).
– Level 2: Analysis. Properties are perceived, but are isolated and unrelated.
Students should recognize and name properties of geometric figures (e.g., “I know it’s a rectangle because it is closed; it has four sides and four right angles, and opposite sides are parallel.”).
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
All students should
Develop strategies to sort and/or group plane geometric figures and refine the vocabulary used to explain their strategies.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Describe a circle.
Trace triangles, squares, rectangles, and circles.
Describe triangles, squares, and rectangles by the number of sides, vertices, and right angles.
Sort plane geometric figures into appropriate subsets
(categories) based on characteristics (number of sides, vertices, angles, curved, etc.).
Identify the name of the geometric figure when given information about the number of sides, vertices, and right angles.
35
Students should have experiences with various plane geometric polygons.
– Triangles could be equilateral, right, obtuse, acute, etc.
–
Quadrilaterals could be rectangles, squares, trapezoids, rhombi, etc.
A vertex is the point at which two line segments, lines, or rays meet to form an angle.
A polygon is a plane geometric figure which
– has sides that are line segments;
– is simple (its sides do not cross);
– is closed; and
– is two-dimensional (lies in a plane).
A triangle is a polygon with three angles and three sides.
A quadrilateral is a polygon with four sides.
A rectangle is a quadrilateral with four right angles.
A square is a rectangle with four sides of equal length.
A circle is a closed curve with all points in one plane and the same distance from a fixed point
(the center).
Transformations (translations, reflections, and rotation) can be used to change the location of objects
Presentation of triangles, rectangles, and squares should be made in a variety of spatial orientations so that students do not develop the common misconception that triangles, rectangles, and squares must have one side parallel to the bottom of the page on which they are printed.
Accomack County Schools Curriculum Guide
First Grade Mathematics
36
Accomack County Schools Curriculum Guide
First Grade Mathematics
SOL 1.12 Continued
Teacher Resources:
Text:
SBG Mathematics 1999
Big Book Stitching Stories
Chapter / Lesson, page 5.3, p. 133-134, 5.4, p. 135-136
Text: Saxon Math Second Edition
Lesson 6, 13, 24
Aims: Fall Into Math and Science “You Drive Me Crackers,” pg. 61-68; “Shape Up”, pg. 69-72
Manipulatives: pattern blocks, geo boards
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : A Kiss is Round by Blossom Budney, Beginning to Learn About Shapes by
Richard Allen, Finding Out About Shapes by Mae Freeman, Shapes to Show by Karen Gundersheimer,
The Tangram Magician by Lisa and Lee Ernst, The Village of Round and Square Houses by A. Grifalconi,
Are You a Square? by E. Kessler and L. Kessler, Circles, Triangles, and Squares by Tana Hoban, Shapes by
Richard Allington, The Parade of Shapes by Sylvia Tester, Triangles, Squares, Circle by William Wegman,
Shapes, Shapes, Shapes by Tana Hoban, The Shapes Game by Paul Rogers and Sian Tucker, The Greedy
Triangle by Marilyn Burns, The Cricket in Times Squares by George Selden, The Village of Round and
Square Houses by Ann Grifalconi.
Virginia Department of Education Training Modules: Geometry—Section 1 “The van Hiele Levels of
Geometry Understanding” activity; Section 1 “Quadrilaterals and their Properties” activity; Section 1
“Quadrilateral Sort” activity; Section 1 “What’s My Rule” activity; Section 1 “Quadrilateral Sorting
Laboratory”; Section 1 “Quadrilaterals and their Properties Through LOGO” activity; Section 2 “Human
Circle” activity; Section 2 “Geoboard Triangles and Quadrilaterals” activity; Section 3 “Square It” activity;
Section 3 “Pick Up the Sticks” activity; Section 3 “Make Your Own Tangrams” activity; Section 3
“Symmetry & Right Angles in Quadrilaterals” activity; Section 3 “Origami: Making a Square” activity;
Section 3 “Origami: Making a Heart” activity;
Section 4 “Sums of Angles of a Triangle” activity; Section 4 “Do Congruent Triangles Tessellate?” activity; Section 5 “Dominoes & Triominoes” activity; Section 5 “Tetrominoes” activity; Section 5
“Pentominoes” activity; Section 5 “Areas with Pentominoes” activity; Section 5 “Hexominoes” activity;
Section 5 “Perimeters with Hexominoes” activity
Instructional Vignette: (Alternate Teaching Strategies)
Provide students with a pattern block or attribute block outline puzzle. Direct the child to use any combination of blocks to fill in the picture. Help the children to discover a
37
Accomack County Schools Curriculum Guide
First Grade Mathematics relationship between the sides and corners of the adjoining blocks and the completion of the outline picture.
Ask children to draw shapes such as squares, rectangles and circles in the air and on the chalkboard with their fingers. Encourage the children to then use their pencils and draw these shapes on paper. Finally, help children to transfer their acquired knowledge by creating shapes on geo-boards with rubber bands.
Give students attribute blocks. Read riddles that describe a particular shape. Ask the students to determine the shape and share their choice with a partner as well as their reasoning.
Create shapes by connecting dots on paper.
Ask children to work with a partner. Model for students that one child will point to a face on a solid and the other child will then predict the shape that would be made by tracing that face. Tell children to check their prediction by tracing the face. Repeat this activity until all children have drawn a circle, a triangle, a square, and a rectangle. When children have drawn each shape, they identify the shapes by name.
Shape Monsters: Create some shape monsters. Create two dice. One has body parts (eyes, nose, mouth, arms, legs, body). One has shapes (triangle, circle, square, rectangle). Give each child a monster and pair them up to play the game. The child rolls the two dice. If their monster has the combination they rolled (ie: square eyes) they trace/color that on their monster. The first child to color their whole monster wins.
Additional Vocabulary: triangle - A polygon with three sides and three angles. rectangle - A quadrilateral with two pairs of congruent, parallel sides and four right angles. square - A parallelogram with four congruent sides and four right angles. circle - A plane figure with all points the same distance from a fixed point called the center.
Figure
Plane figure
Vertices
Right angle sides
38
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.13 The student will construct, model, and describe objects in the environment as geometric shapes (triangle, rectangle, square, and circle) and explain the reasonableness of each choice.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Representations of circles, squares, rectangles, and triangles can be found in the students’ environment at school and at home. Students should have opportunities to identify/classify things in their environment by the type of figure those things represent.
A common misconception students have when a figure such as a square is rotated is they will frequently refer to the rotated square as a diamond. Clarification needs to be ongoing — i.e., a square is a square regardless of its location in space; there is no such geometric figure as a diamond.
Building geometric and spatial capabilities
fosters enthusiasm for mathematics while
providing a context to develop spatial sense.
Polygons can be constructed using other polygons (e.g., six equilateral triangles can be used to construct a hexagon, a triangle can be added to a rectangle to create a pentagon, etc.).
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
All students should
Understand that geometric figures are integral parts of the environment.
Use familiarity with the figure, structure, and location to develop spatial reasoning.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Construct plane geometric figures.
Identify models of representations of circles, squares, rectangles, and triangles in the environment at school and home and tell why they represent those figures.
Describe representations of circles, squares, rectangles, and triangles in the environment and explain the reasonableness of the choice.
39
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.13 Continued
Teacher Resources:
Texts: SBG Mathematics 1999 & Saxon Math Second Edition
Lessons in text did not correlate with Virginia Standard of Learning 1.17
Aims: Fall Into Math and Science “You Drive Me Crackers,” pg. 61-68; “Shape Up,” pg. 69-72; “Shape
Town”
Manipulatives: See SOL 1.12
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : Dots, Spots, Speckles and Stripes by Tana Hoban, Patchwork Quilt by Valerie
Flournoy, Round & Round & Round by Tana Hoban, The Village of Round and Square Houses by Anne
Grifalconi, Take Off With Shapes by Sally Hewitt, The Shape Game by Paul Rogers, Grandfather Tang’s
Story by Ann Tompert
Virginia Department of Education Training Modules: Geometry—Section 2 “Shape Hunt” activity
Instructional Vignette: (Alternate Teaching Strategies)
Divide a piece of paper into fourths. Label the sections with square, circle, triange and rectangle. Have the students search the room for objects that they can draw under each shape. After filling in the paper, have them share why the said each object was a
certain shape (justify with number of sides, vertices and right angles).
Additional Vocabulary: triangle - A polygon with three sides and three angles. rectangle - A quadrilateral with two pairs of congruent, parallel sides and four right angles. square - A parallelogram with four congruent sides and four right angles. circle - A plane figure with all points the same distance from a fixed point called the center.
Figure
Plane figure
Vertices
Right angle sides
40
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.14 The student will investigate, identify, and describe various forms of data collection (e.g., recording daily temperature, lunch count, attendance, favorite ice cream), using tables, picture graphs, and object graphs.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Students’ questions about the physical world can often be answered by collecting data and observing the results.
Data are information collected about people or things. The primary purpose of collecting data is to answer questions.
After generating questions, students decide what information is needed and how it can be collected.
The collection of the data often leads to new questions to be investigated.
The entire process broadens children’s views of mathematics and its usefulness.
Data collection could involve voting, informal surveys, tallying, and charts.
Surveys, which are data-collecting tools that list choices, should have a limited number of questions at the primary grades.
Tallying is a method for gathering information.
Tally marks are used to show how often something happens or occurs. Each tally mark represents one occurrence. Tally marks are clustered into groups of five, with four vertical marks representing the first four occurrences and the fifth mark crossing the first four on a diagonal to represent the fifth occurrence.
ESSENTIAL UNDERSTANDINGS
All students should
Understand how data can be collected and presented in an organized manner.
Understand that data gathered and analyzed from observations and surveys can have an impact on our everyday lives.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Investigate various forms of data collection, including counting and tallying, informal surveys, observations, and voting.
Identify and describe various forms of data collection in practical situations (e.g., recording daily temperature, lunch count, attendance, and favorite ice cream.)
41
Accomack County Schools Curriculum Guide
First Grade Mathematics
SOL 1.14
Teacher Resources:
Text: SBG Mathematics 1999
Chapter / Lesson, page 1.5, p. 9-10, 1.15, p. 29-30, 8.6, p. 237-238, 9.11, p. 271-272
Text : Saxon Math Second Edition
Lesson 5, 7, 10, 19, 38, 40, 65, 82, 118
Aims: Glide Into Winter With Math and Science “Do You Have a Snoot for Fruit”, pg. 58-67; “Valentine
Candy Count,” pg. 35-41; “Electric Breakfast I” 29-31; “Electric Breakfast II”, pg. 32-34; “Mighty
Mittens,” pg. 25-28; “How Does Your Corn Pop?,” pg. 5-10;
“Whoa—That’s Heavy ”, pg. 71-73; Spring Into Math and Science “Feet Findings,” pg. 38-41;
Fall Into Math and Science “Apples A Peel To Me”; “Going Nuts”; “Bunches of Lunches,”
Magazine Volume 5 Issue 2
Manipulatives: chart paper, pictures for graphs
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : Anno’s Math Games II by Mitsumasa Anno, Anno’s Math Games III by
Mitsumasa Anno, Caps for Sale by Esphyr Slobodkina, Elephant Buttons by Veno, The M & M Counting
Book by Barbara Barbiari McGrath, Frog and Toad Are Friends by Arnold Lobel, In the Tall, Tall Grass by
Denise Fleming
Virginia Department of Education Training Modules: Probability and Statistics—Section 1, Activity 1
“Sandwich Problem”; Section 1, Activity 2 “Why is Probability and Statistics Important?”; Section 1,
Activity 3 “The Big Ideas of Probability and Statistics”; Section 1, Activity 4 “What are the Goals of the
Institute?”; Section 1, Activity 1 “Collecting Data: Count the Ways”; Section 2, Activity 2 “Random
Sampling”
Instructional Vignette: (Alternate Teaching Strategies)
Record daily temperature and weather. Help students to compare the information shown and record tow sentences about what they discover.
Encourage students to survey their classmates to determine preferences for things such as food, flavors of ice cream, shoes, clothing and toys. Help children record their preferences in a picture or object graph and write at least two sentences about what they discover. Examples might include: More boys in our class are wearing tennis shoes than girls.
42
Accomack County Schools Curriculum Guide
First Grade Mathematics
Have the children draw a picture on an index card to show how they came to school. Ask the children to create a graph by sorting the information and attaching the cards to a large piece of paper.
Additional Vocabulary: data - Information especially numerical information. tally - A method of gathering information. tally marks - Marks made to keep track of things being counted.
Picto(picture)graph
Object graph
Table
Survey
43
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.15 The student will interpret information displayed in a picture or object graph, using the vocabulary more, less, fewer, greater
than, less than, and equal to.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Statistics is used to describe and interpret with numbers the world around us; it is a tool for problem solving.
Students’ questions about everyday life can often be answered by collecting and interpreting data.
Organized data provides a clearer picture for interpretation. Data may be described in object graphs and picture graphs.
Picture graphs are graphs that use pictures to show and compare information.
Object graphs are graphs that use concrete materials to represent the categorical data that are collected (e.g., cubes stacked by the month, with one cube representing the birthday month of each student).
Interpretation of the data could lead to additional questions to be investigated.
ESSENTIAL UNDERSTANDINGS
All students should
Understand that picture graphs use pictures to represent and compare data while object graphs use concrete objects to represent and compare data.
Understand that data can be analyzed and interpreted, using the terms more , less , fewer , greater than , less than , and equal to .
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Compare one category to another in a graph, indicating which has more or which has less, or which is equal to.
Interpret information displayed in object graphs and picture graphs, using the words more , less , fewer , greater than , less than , and equal to .
Find answers to questions, using graphs (e.g., “Which category has more?”, “How many more?”, and “How many in all?”).
44
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.15 Continued
Teacher Resources:
Text: Silver Burdett Ginn 1999
1.15, p. 29-30; 8.6, p. 237-238
Aims: Glide Into Winter With Math and Science “Do You Have A Snoot for Fruit,” pg. 58-67; “Valentine
Candy Count,” pg. 35-41; “Electric Breakfast I,” pg. 29-31; “Electric Breakfast II,” pg. 32-34; “Mighty
Mittens,” pg. 25-28; “How Does Your Corn Pop?,” pg. 5-10; “Polar Bear Pie,” pg. 19-21; “Goober Peas,” pg. 22-24; “You Are All Heart,” pg. 42-44; Fall Into Math and Science “How Tall Are You?,” pg. 11-17;
“A Weigh We Go,” pg. 18-21; “Fall Leafs Me Happy,” pg. 37-41; “You Can Count On Us,” pg. 1-4; “An
Eye for Color,” pg. 5-10
Manipulatives: chart paper, pictures for graphs
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
, Renaissance Place
Children’s Literature : Anno’s Hat Tricks by Mitsumasa Anno, Guess Who My Favorite Person Is by
Byrd Baylor, Alligator Shoes by Arthur Dorros, The Button Box by Margarette Reid, What Will The
Weather Be Like Today? by Paul Rodgers, Who’s Hat is That? by Ron Roy, Whose Shoes are These? by
Ron Roy, Lemonade for Sale by Stuart Murphy, Tiger Math Learning to Graph from a Baby Tiger by Ann
Whitehead Nagda and Cindy Bickel
Virginia Department of Education Training Modules: Probability and Statistics—Section 1, activity 1
“Sandwich Problem”; Section 1, activity 2 “Why is Probability and Statistics Important?”; Section 1, activity 3 “The Big Ideas of Probability and Statistics”; Section 1, activity 4 “What are the Goals of the
Institute?”; Section 1, activity 5 “Sixth Grade Mystery Data”; Section 1, activity 6 “Posing Questions” ;
Section 2, activity 5 “What’s Missing”; Section 2, activity 5 “What’s Missing”; Section 2, activity 6
“Object Graphs and Picture Graphs”; Section 3, activity 7 “Graph Detective”; Section 4, activity 5
“Graphical Interpretations”; Section 4, activity 6B “Matching Game: Graphs, Data, Summary”; Section 4, activity 8 “Draw the Graph Game”
Instructional Vignette: (Alternate Teaching Strategies)
Pass out snack bags of M & Ms. Ask the students to open the bags and sort the candies into sets according to color. Tell the children to line their candies in rows according to the colors to indicate which child has more, less or equal amounts of the same color. Allow the students to eat the candy after a class discussion and the writing of two sentences that describe what the children discover.
Use attributes such as eye color to create pictorial graphs. Ask the students to draw a picture of their eyes and color them correctly. Direct the students to glue the picture of their eyes to a large piece of paper complete with columns or rows. Help the children to read the pictorial graph to determine which eye color is prevalent. Which eye color is the least prevalent among members of the class. Are any eye colors represented equally?
45
Accomack County Schools Curriculum Guide
First Grade Mathematics
Ask each child to color a Post-It Note ice cream shape to represent their favorite flavor of ice cream.
Direct the students to then place their note on a teacher made grid. Repeat the activity with story characters.
Allow students to cut out pictures in magazines, group the pictures and then graph the pictures on their own to make a pictorial graph. Have students describe their graph to a partner.
Additional Vocabulary: data - Information especially numerical information. tally - A method of gathering information. tally marks - Marks made to keep track of things being counted.
Picto(picture)graph
Object graph
Table
Survey
More
Less
Fewer
Greater than
Less than
Equal to
46
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.16 The student will sort and classify concrete objects according to one or more attributes, including color, size, shape, and thickness.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Sorting, classifying, and ordering objects facilitate work with patterns, geometric shapes, and data.
To classify is to arrange or organize a set of materials according to a category or attribute (a quality or characteristic).
General similarities and differences among items are easily observed by primary students, who can begin to focus on more than one attribute at a time. During the primary grades, the teacher’s task is to move students toward a more sophisticated understanding of classification in which two or more attributes connect or differentiate sets, such as those found in nature
(e.g., leaves with different colors and different shapes).
ESSENTIAL UNDERSTANDINGS
All students should
Understand the same set of objects can be sorted and classified in different ways.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Sort and classify objects into appropriate subsets
(categories) based on one or two attributes, such as size, shape, color, or thickness.
47
Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.16 Continued
Teacher Resources:
Text: Silver Burdett Ginn (1999)
Aims: Fall Into Math and Science “You Can Count On Us,” pg. 1-4; “An Eye for Color,” pg. 5-10; “Weather
Wear,” pg. 22-24; “Apples A Peel to Me,” pg. 46-49; “Flowers,” pg. 84-86; “Shape Up”; Primarily Bears
“Gummy Bears,” pg. 59-64; “M & M Math,” pg. 65-68
Manipulatives: foam attribute blocks, buttons, other objects to sort
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : A House for Hermit Crab by Eric Carle, Another, Another, and More by Marion
Walter, Each Peach, Pear, Plum by Ahlberg, The Patchwork Quilt by Valerie Flourney, The Turnabout, Think
About, Look About Book by Duncan Gardner, The Mirror Puzzle Book by Marion Walter, Frog and Toad by
Arnold Lobel, Sorting by Peter Patilla, Mixing and Matching by Nicola Tuxworth
Virginia Department of Education Training Modules: Geometry—Section 2 “What’s In the Box?” activity; Section 2 “Missing Pieces” activity; Section 2 “What’s My Rule” activity; Section 2 “Twenty
Questions Game” activity; Section 2 “Who Am I?” activity; Section 2 “Differences-Trains & Games” activity; Section 2 “Hidden Number Patterns”; Section 2 “Attribute Networks” activity
Instructional Vignette: (Alternate Teaching Strategies)
Provide students with a variety of manipulatives to sort and classify. Put these items in a center for the students to use during their free center time. Provide guided practice on sorting and classifying during the Every Day Counts activities. Begin with having the student sort by a single attribute such as size, shape or color. When this skill has been mastered, then add an additional attribute. Increase the difficulty as each level is mastered.
Use sorting trays to practice classifying objects into sets according to common attributes. Set one tray on each table and ask the children to sort the objects. Ask partners to share how and why they sorted them as they did. Ask them if there is any other way the objects could be sorted. Change the objects being sorted and repeat the activity.
Pass out paper shapes and a large sheet of newsprint. Ask the students to sort the shapes by one attribute and glue them down. Have the children share which attribute they used to sort the shapes.
Additional Vocabulary: classify - To arrange or organize a set of materials according to a category or attribute. attribute
48
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.17 The student will recognize, describe, extend, and create a wide variety of growing and repeating patterns.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Patterns allow children to recognize order, generalize, and predict.
Patterning should include
– reproducing a given pattern, using manipulatives;
– recording a pattern with pictures or symbols;
– transferring a pattern into a different form or different representation (e.g., blue–blue– red to an AAB repeating pattern); and
– analyzing patterns in practical situations (e.g., calendar, seasons, days of the week).
The simplest types of patterns are repeating patterns. The part of the pattern that repeats is the core. The patterns can be oral, such as the refrain in “Old MacDonald’s Farm” (“e-i-e-i-o”), or physical with clapping and snapping patterns, or combinations of both, such as is found in songs like the “Hokey Pokey.” In each case, students need to identify the basic unit of the pattern and repeat it. Opportunities to create, recognize, describe, and extend repeating patterns are essential to the primary school experience.
Growing patterns are more difficult for students to understand than repeating patterns because not only must they determine what comes next, they must also begin the process of generalization.
Students need experiences with growing patterns in both arithmetic and geometric formats.
ESSENTIAL UNDERSTANDINGS
All students should
Understand that patterns are a way to recognize order, to organize their world, and to predict what comes next in an arrangement.
Recognize and state the core of a pattern.
Analyze how both repeating and growing patterns are generated.
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Recognize the pattern in a given rhythmic, color, geometric figure, or numerical sequence.
Describe the pattern in a given rhythmic, color, geometric figure, or numerical sequence in terms of the core (the part of the sequence that repeats).
Extend a pattern, using manipulatives, geometric figures, numbers, or calculators.
Transfer a pattern from one form to another.
Create a repeating or growing pattern, using manipulatives, geometric figures, numbers, or calculators (e.g., the growing patterns 2, 3, 2, 4, 2, 5, 2, 6, 2,
).
49
Create an arithmetic number pattern. Sample numeric patterns include
– 6, 9, 12, 15, 18,
(growing pattern);
– 20, 18, 16, 14,
(growing pattern);
– 1, 2, 4, 7, 11, 16,
(growing pattern); and
– 1, 3, 5, 1, 3, 5, 1, 3, 5… (repeating pattern).
In geometric patterns, students must often recognize transformations of a figure, particularly rotation or reflection. Rotation is the result of turning a figure around a point or a vertex, and reflection is the result of flipping a figure over a line.
Accomack County Schools Curriculum Guide
First Grade Mathematics
50
Accomack County Schools Curriculum Guide
First Grade Mathematics
SOL 1.17 Continued
Teacher Resources:
Text: SBG, 1999
1.3, p. 5-6; 1.7, p. 13-14; 1.13, p. 25-26; 5.6, p. 139-140
Aims: Fall Into Math and Science “Going Nuts”
Manipulatives: pattern blocks, unifix cubes, buttons, magnetic numbers/letters
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
,
Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : A Friend is Someone Who Likes You by Joan Walsh Anglund,
Brown Bear, Brown Bear, What Do You See? by Eric Carle and Bill Martin, Jr., Drummer
Hoff by Barbara Emberley, Fortunately by Remy Charlip, If It Weren’t For You by Charlotte
Zolotow, Polar Bear, Polar Bear, What Do You See? by Eric Carle and Bill Martin, Jr.,
Someday by Charlotte Zolotow, The Very Busy Spider by Eric Carle, One Hundred is a
Family by Pam Manoz, Discovering Patterns by Andrew King, Mixing and Matching by
Nicola Tuxworth
Virginia Department of Education Training Modules:
Geometry—Section 3 “Partition the Square” activity
Patterns, Functions & Algebra—Section 1, activity 1 “Creating and Identifying Patterns
(Warm-up)”; Section 1, activity 2 “The Big Ideas of Algebra”; Section 1, activity 3 “Why is
Algebraic Thinking Important?”; Section 1, activity 4 “Libby (Warm Up) What’s In the
Box?”; Section 2, activity 1A “I Need a Necktie, Please ” ; “Section 2, Activity 1B “Up, Up and Away ”; Section 2, activity 2A “Tons of Tunnels”; Section 2, Activity 3A “The Jeweled
Snake”; Section 2, activity 4D “Odd and Even”; Section 2, activity 4G “Arrow Math’
Instructional Vignette: (Alternate Teaching Strategies)
Ask students to create patterns of color, size or shape using stringing beads or linking cubes. Ask the children to determine what will come next in the pattern.
Use unifix cubes to create trains of color patterns.
Use songs and fingerplays such as Hand Jive, Over in the Meadow, Cat Goes Fiddle-I-
Fee to help students understand how to extend and repeat patterns.
Additional Vocabulary:
51
Accomack County Schools Curriculum Guide
First Grade Mathematics
Pattern— A way to recognize order. To predict what comes next in an arrangement.
Repeating pattern
Repeating part
Growing pattern
Geometric figure
Core of pattern
52
Accomack County Schools Curriculum Guide
First Grade Mathematics
1.18 The student will demonstrate an understanding of equality through the use of the equal sign.
UNDERSTANDING THE STANDARD
(Background Information for Instructor Use
Only)
Equality can be shown by measuring with a balance scale or a number balance.
Manipulatives such as rods, connecting cubes, and counters can be used to model equations.
An expression is a representation of a quantity. It is made up of numbers, variables, and/or computational symbols. It does not have an equal sign (e.g., x + 3).
An equation is a mathematical statement that two expressions are the same. Equations are written with an equal sign .
Equations have expressions of equal value on both sides (e.g., 5 + 3 = 8, 8 = 5 + 3 and 4 + 3 = 9 - 2).
An equation can be represented using balance scales. There must be the same amount on each side of an equal sign (e.g., 5 + 3 = 3 + 5 ).
A common misunderstanding is that the equal sign always means the answer. The equal sign can represent an equality.
Equations should be shown in many different forms (e.g., 6 = 6, 4 + 2 = 6, 5 + 1 = 4 + 2,
6 = 4 + 2, 4 = 6 - 2).
Inequalities such as 5 < 4 + 3 are not equations.
ESSENTIAL UNDERSTANDINGS
All students should
Understand that the equal sign means “is the same as” or “another name for” or “equal in value”.
Understand that equality represents a balance concept. Both sides of the equation balance because they are equal (they have the same value).
ESSENTIAL KNOWLEDGE AND SKILLS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
Identify the equality (=) symbol.
Recognize that the equations 4 + 2 = 2 + 4 and 6 + 1= 4 + 3 represent the relationship between two expressions of equal value.
Model an equation that represents the relationship of two expressions of equal value.
Identify equivalent values (e.g., 3 = 3, 4 + 3 = 8 - 1,
7 = 2 + 5, etc.).
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Equations must have the equal sign.
It is important for children to understand that the expression 3 + 5 is another representation of eight.
The equal sign is used when two representations name the same number, 5 + 3 = 10 - 2. These two expressions in the equation represent the same number, eight.
Equations should be routinely modeled in conjunction with story problems.
Solving missing addend problems and stories helps with the understanding of equality and the equal sign (e.g., There are 4 red birds in the tree.
Some black birds fly to the tree. Now there are six birds in the tree. How many black birds flew to the tree? 4+__ =6)
Accomack County Schools Curriculum Guide
First Grade Mathematics
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Accomack County Schools Curriculum Guide
First Grade Mathematics
Standard 1.18 Continued
Manipulatives: number balance scales, balance scale, objects to measure, containers
Technology: www.computerlabkids.com
, www.apples4teachers.com/math.html
, www.lovetoknow.com/top10/kids_math.html
, www.hbschool.com
, www.quia.com
, Education City, www.mathcats.com
, www.solteacher.com
Children’s Literature : Equal Schmequal by Virginia Kroll
Instructional Vignette: (Alternate Teaching Strategies)
Domino Go Fish – give students dominos (or paper copies of dominos). Have them put them face down on the table. Students play the game in pairs. Each child picks two dominos. It they are equal, they record it on their paper and write the number sentence for each domino. If they are not equal, their turn is over and the next student goes.
Additional Vocabulary:
Equal sign
Equality symbol
Balance concept
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