MADISON PUBLIC SCHOOL DISTRICT
Kindergarten Mathematics
Authored by: Susan Corea and Valerie Cristiano
Updated by: Kathryn Lemerich
Reviewed by: Lee Nittel,
Director of Curriculum and Instruction
Updated with Common Core State Standards: Fall 2012
Members of the Board of Education:
Lisa Ellis, President
Patrick Rowe, Vice-President
David Arthur
Kevin Blair
Shade Grahling
Linda Gilbert
Thomas Haralampoudis
James Novotny
Superintendent: Dr. Michael Rossi
Madison Public Schools
359 Woodland Road, Madison, NJ 07940
www.madisonpublicschools.org
I. OVERVIEW
The K-5 mathematics curriculum is to provide students with a strong content base in mathematics while
promoting and instilling the skills of problem solving, communication in mathematics, making mathematical
connections, and reasoning. Throughout the delivery of the K-5 mathematics program, various tools and
technology are employed, including manipulatives, calculators, software, websites, and computers. A strong
focus of the program in on promoting high levels of mathematical thought through experiences which extend
beyond traditional computation. The program is directly correlated to the Common Core State Standards
and is designed to adequately prepare students for the NJ state assessments.
II.
RATIONALE
The K-5 mathematics program mission is to provide students with content-specific skills and concepts while
developing problem-solving skills and strategies, communication, and reasoning. Lessons are prepared and
implemented developmentally, sequentially and with the understanding that learning proceeds from concrete
to abstract levels.
III.
STUDENT OUTCOMES (Linked to the Common Core State Standards for Mathematics)
Chapter 1: Sorting and Classifying
Measurement and Data (K.MD)
Classify objects and count the number of objects in each category.
K.MD.3: Classify objects into given categories; count the numbers of objects in each category and sort the
categories by count. Limit category counts to be less than or equal to 10.
Chapter 2: Patterns
Measurement and Data (K.MD)
Classify objects and count the number of objects in each category.
K.MD.3: Classify objects into given categories; count the numbers of objects in each category and sort the
categories by count. Limit category counts to be less than or equal to 10.
Chapter 3: Numbers 0 – 5
Counting and Cardinality (K.CC)
Know number names and the count sequence.
K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to
begin at 1).
K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0
representing a count of no objects).
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Count to tell the number of objects.
K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality.
a. When counting objects, say the number names in the standard order, pairing each object with one
and only one number name and each number name with one and only one object.
b. Understand that the last number name said tells the number of objects counted. The number of
objects is the same regardless of their arrangement or the order in which they were counted.
c. Understand that each successive number name refers to a quantity that is one larger.
K.CC.5: Count to answer “how many?” questions about as many as 20 things arranged in a line, a
rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20,
count out that many objects.
Compare numbers.
K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the
number of objects in another group, e.g., by using matching and counting strategies.1
1Include groups with up to ten objects.
K.CC.7: Compare two numbers between 1 and 10 presented as written numerals.
Chapter 4: Numbers 6 – 12
Counting and Cardinality (K.CC)
Know number names and the count sequence.
K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to
begin at 1).
K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0
representing a count of no objects).
Count to tell the number of objects.
K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality.
a. When counting objects, say the number names in the standard order, pairing each object with one
and only one number name and each number name with one and only one object.
b. Understand that the last number name said tells the number of objects counted. The number of
objects is the same regardless of their arrangement or the order in which they were counted.
c. Understand that each successive number name refers to a quantity that is one larger.
K.CC.5: Count to answer “how many?” questions about as many as 20 things arranged in a line, a
rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20,
count out that many objects.
Compare numbers.
K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the
number of objects in another group, e.g., by using matching and counting strategies.1
1Include groups with up to ten objects.
3
K.CC.7: Compare two numbers between 1 and 10 presented as written numerals.
Measurement and Data (K.MD)
Classify objects and count the number of objects in each category.
K.MD.3: Classify objects into given categories; count the numbers of objects in each category and sort the
categories by count. Limit category counts to be less than or equal to 10.
Chapter 5: Calendars and Clocks
Chapter 6: Measurement and Money
Measurement and Data (K.MD)
Describe and compare measurable attributes.
K.MD.1: Describe measurable attributes of objects, such as length or weight. Describe several measurable
attributes of a single object.
K.MD.2: Directly compare two objects with a measurable attribute in common, to see which object has
“more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two
children and describe one child as taller/shorter.
Classify objects and count the number of objects in each category.
K.MD.3: Classify objects into given categories; count the numbers of objects in each category and sort the
categories by count. Limit category counts to be less than or equal to 10.
Chapter 7: Addition
Operations and Algebraic Thinking K.OA
Understand addition as putting together and adding to, and understand subtraction as taking apart and
taking from.
K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g.,
claps), acting out situations, verbal explanations, expressions, or equations. 2Drawings need not show details,
but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the
Standards.)
K.OA.2: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using
objects or drawings to represent the problem.
K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects
or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g.,
by using objects or drawings, and record the answer with a drawing or equation.
K.OA.5: Fluently add and subtract within 5.
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Chapter 8: Subtraction
Operations and Algebraic Thinking K.OA
Understand addition as putting together and adding to, and understand subtraction as taking apart and
taking from.
K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g.,
claps), acting out situations, verbal explanations, expressions, or equations. 2Drawings need not show details,
but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the
Standards.)
K.OA.2: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using
objects or drawings to represent the problem.
K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects
or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g.,
by using objects or drawings, and record the answer with a drawing or equation.
K.OA.5: Fluently add and subtract within 5.
Chapter 9: Geometry and Fractions
Geometry K.G
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and
spheres).
K.G.1: Describe objects in the environment using names of shapes, and describe the relative positions of
these objects using terms such as above, below, beside, in front of, behind, and next to.
K.G.2: Correctly name shapes regardless of their orientations or overall size.
K.G.3: Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
Analyze, compare, create, and compose shapes.
K.G.4: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using
informal language to describe their similarities, differences, parts (e.g., number of sides and
vertices/“corners”) and other attributes (e.g., having sides of equal length).
K.G.5: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and
drawing shapes.
K.G.6: Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides
touching to make a rectangle?”
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Chapter 10: Greater Numbers
Counting and Cardinality (K.CC)
Know number names and the count sequence.
K.CC.1: Count to 100 by ones and by tens.
K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to
begin at 1).
K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0
representing a count of no objects).
Count to tell the number of objects.
K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality.
a. When counting objects, say the number names in the standard order, pairing each object with one
and only one number name and each number name with one and only one object.
b. Understand that the last number name said tells the number of objects counted. The number of
objects is the same regardless of their arrangement or the order in which they were counted.
c. Understand that each successive number name refers to a quantity that is one larger.
K.CC.5: Count to answer “how many?” questions about as many as 20 things arranged in a line, a
rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20,
count out that many objects.
Compare numbers.
K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the
number of objects in another group, e.g., by using matching and counting strategies.1
1Include groups with up to ten objects.
K.CC.7: Compare two numbers between 1 and 10 presented as written numerals.
Number and Operations in Base Ten (K.NBT)
Work with numbers 11–19 to gain foundations for place value.
K.NBT.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by
using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18
= 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven,
eight, or nine ones.
IV.
ESSENTIAL QUESTIONS AND CONTENT
Chapter 1: Sorting and Classifying
1. Using positional words to show where objects are.
2. Sort objects by one of the three attributes: color, size and shape.
3. Using a bar graph for information
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Chapter 2: Patterns
1. What is a pattern? Demonstrating different types of patterns (sound, motion, objects)
2. What “name” will be given to a pattern?
3. Continuing the objects of patterns
Chapter 3: Numbers 0 – 5
1. What are equal sets?
2. Count and write numbers 0 – 5
3. What are ordinal numbers?
Chapter 4: Numbers 6 – 12
1. Count, write and order numbers 0 – 12
2. What is estimation?
Chapter 5: Calendars and Clocks
1. What are the seven days of the week?
2. What are the twelve months of the year?
3. What time is it? (to the hour)
Chapter 6: Measurement and Money
1. How to measure lengths, width and capacities
2. Identify coins and their values (penny, nickel and dime)
Chapter 7: Addition
1. Adding two numbers to the sum of 10
2. Writing a number sentence
Chapter 8: Subtraction
1. Subtraction through 10
2. Writing a number sentence
3. Determining the process: to add or subtract
Chapter 9: Geometry and Fractions
1. Recognizing the basic plane shapes
2. Recognizing three dimensional shapes
3. What is symmetry?
4. What is one half?
Chapter 10: Greater Numbers
1. Identify and write numbers 10 - 30
2. What is a set of ten?
3. What is “counting on”?
4. Estimating quantities with sets of ten
V. STRATEGIES
Students will be involved in cooperative learning and individual study throughout mathematics instruction.
Much of the instruction will incorporate problem-based learning, including hands-on activities,
manipulatives, projects, and class discussions, as well as other strategies determined by the teacher.
▪ Given a group of individual problem-solving situation, students will use a variety of mathematical
perceptions such as seeing patterns, making comparisons, estimating amounts, etc. to deduce a
solution.
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▪
▪
▪
Given a set of oral or written problems, students will understand the mathematical context,
recognize the operative significance of the symbols, and calculate the solutions.
Given manipulatives, games, models, calculators, and other technology, students will solve
problems appropriate to the unit or skill being studied.
Differentiated Instruction is a key component to mathematics instruction. See Appendix A (to be
added in summer 2009) for grade specific activities and lessons.
VI. EVALUATION
Students’ learning will be evaluated regularly in the following manner:
▪ Teacher observation
▪ District math assessments: Cumulative
Math Assessment (May)
▪ End of chapter tests
▪ Anecdotal records
V11. REQUIRED RESOURCES
Text: Houghton Mifflin Mathematics, Teacher’s Edition, Kindergarten level, Volumes I and II. Houghton
Mifflin Company, Boston / Morris Plains, NJ. 2002
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Houghton Mifflin Practice Workbook
Houghton Mifflin Challenge Workbook
Houghton Mifflin assortment of manipulatives
Supplemental Resources: Literature suggestions
Patterns
The Quilt Story by Tony Johnston and Tomie DePaola
Caps for Sale by Esphyr Slobodkina
Numbers and Counting
Feast for 10 by Cathryn Falwell
When Sheep Sleep by Laura Numeroff
Let’s Count It Out, Jesse Bear by Nancy White Carlstrom
Each Orange Had 8 Slices by Paul Giganti, Jr.
Fish Eyes by Lois Ehlert
Calendars and Clocks
What Time Is It, Mr. Crocodile by Judy Sierra
The Grouchy Ladybug by Erick Carle
Today is Monday by Eric Carle
Measurement and Money
Inch by Inch by Leo Lionni
Alexander, Who Used to Be Rich Last Sunday by Judith Viorst
A Chair for My Mother by Vera B. Williams
Addition and Subtraction
Mouse Count by Ellen Stoll Walsh
Rooster’s Off the See the World by Eric Carle
Five Little Ducks by Aruego and Dewey
Roll Over! By Merle Peek
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Geometry and Shapes
The Greedy Triangle by Marilyn Burns
VIII. SCOPE AND SEQUENCE
Chapter 1
Sorting and Classifying
Chapter 2
Patterns
Length of unit: 16 lessons, 3 weeks
Introductory story: A Red Day for Tony
Lesson 1 Positions: top, middle, bottom
Lesson 2 Positions: before, after, between
Lesson 3 Positions: inside, outside
Lesson 4 Positions: right, left
Quick Check and Cumulative Review
Lesson 5 Compare objects: same and different
Lesson 6 Sort objects by color
Lesson 7 Sort objects by size
Lesson 8 Sort objects by shape
Problem Solving: using properties
Lesson 10 Sort objects to make a graph
Lesson 11 Sort coins to make a graph
Lesson 12 Sort objects to make a graph
Quick Check and Cumulative Review
Chapter Test and Practice game (same or different)
Length of unit: 13 lessons, 3 weeks
Introductory story: Penny the Pilot Goes to Town
Lesson 1 Rhythmic patterns
Lesson 2 Patterns by color
Lesson 3 Patterns by size
Lesson 4 Patterns by shape
Problem Solving: find a pattern, growing patterns
Quick Check and Cumulative Review
Lesson 6 Patterns when the objects changing position
Lesson 7 “Name” the pattern and find patterns that are the same
Lesson 8 Making “like” patterns
Problem Solving: extending patterns
Quick Check and Cumulative Review
Chapter Test and Practice game (name the pattern)
Chapter 3
Numbers 0-5
Length of unit: 17 lessons, 3 ½ weeks
Introductory story: What’s in Jacob’s Sandbox?
Lesson 1 Match objects one to one
Lesson 2 Equal sets of objects
Lesson 3 Sets that contain more objects
Lesson 4 Sets that contain less objects
Problem Solving: draw pictures to show sets of: same, more, less
Quick Check and Cumulative Review
Lesson 6 Numbers one and two
Lesson 7 Number three
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Lesson 8 Number four
Lesson 9 Number five
Lesson 10 The number zero
Lesson 11 Numbers zero to five
Lesson 12 Ordinal numbers first to fifth to show position
Problem Solving: use a graph to show more and less
Quick Check and Cumulative Review
Chapter Test and Practice game (numbers 0-5)
Chapter 4
Numbers 6 – 12
Chapter 5
Calendars and Clocks
Chapter 6
Measurement and Money
Length of unit: 20 lessons, 4 weeks
Introductory story: What Shall I Take on a Trip to the Moon?
Lesson 1 Number six
Lesson 2 Number seven
Lesson 3 Number eight
Lesson 4 Number nine
Lesson 5 Numbers six to nine
Quick Check and Cumulative Review
Lesson 6 Number ten
Lesson 7 Number eleven
Lesson 8 Number twelve
Lesson 9 Numbers ten to twelve
Lesson 10 Put sets of numbers in order
Problem Solving: find a pattern using numbers
Quick Check and Cumulative Review
Lesson 12 Count and sort objects by numbers
Lesson 13 Compare sets by more and less
Lesson 14 Estimating with 12 or less
Problem Solving: using a graph to compare more and less objects
Quick Check and Cumulative Review
Chapter Test and Practice game (practice with numbers 6 – 12)
Length of unit: 16 lessons, 3 weeks
Introductory story: Is It Tonight Yet?
Lesson 1 Activities appropriate for: morning, afternoon and evening
Lesson 2 Days of the week in order including today, tomorrow, yesterday
Lesson 3 Month of the year
Lesson 4 How long or short the time to complete a task
Lesson 5 Sequencing actions
Problem Solving: Using a calendar to find information
Quick Check and Cumulative Review
Lesson 7 A sense of how long a minute and an hour are
Lesson 8 Estimating time
Lesson 9 Telling time to the hour- analog clocks
Lesson 10 Matching times on analog and digital clocks
Lesson 11 Time that everyday events take place
Problem Solving: Figuring out how long it takes to complete an activity
Quick Check and Cumulative Review
Chapter Test and Practice game- using a calendar
Length of unit: 20 lessons, 4 weeks
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Introductory story: Harry Caterpillar and the Tallest Sunflower
Lesson 1 Compare objects using: taller, longer, shorter
Lesson 2 Sort objects by length
Lesson 3 Place objects in order by length: longest, tallest, shortest
Lesson 4 Measuring objects with nonstandard units (cubes)
Lesson 5 Estimate and then measure with nonstandard units
Problem Solving: measure yarn lengths and make a graph
Quick Check and Cumulative Review
Lesson 7 Compare the weight of objects using: light, heavy, lighter, heavier
Lesson 8 Order objects by their weight
Lesson 9 Compare containers to determine which holds more and less
Lesson 10 Order objects by what will hold the most and least
Problem Solving: Estimate and measure
Lesson 12 Sort by temperature using: hot, cold, warm
Quick Check and Cumulative Review
Lesson 13 The penny- one cent
Lesson 14 The nickel- 5 pennies, 5 cents
Lesson 15 The dime- 10 pennies, 10 cents
Quick Check and Cumulative Review
Chapter Test and Practice game- using coins
Chapter 7
Addition
Chapter 8
Subtraction
Length of unit: 15 lessons, 3 weeks
Introductory story: What a Day!
Lesson 1 Demonstrate Addition- sets being combined
Lesson 2 Add 1 to numbers 0 – 5
Lesson 3 Add 1 to numbers 6 – 9
Lesson 4 Writing the addition sentence, plus and equals signs
Problem Solving: Writing the addition sentence from a picture story
Quick Check and Cumulative Review
Lesson 6 Add 2 to numbers 0 – 5
Lesson 7 Add 2 to numbers 6 – 8
Lesson 8 Adding doubles (numbers that are the same number)
Lesson 9 Vertical addition
Lesson 10 Adding with sums to 10
Problem Solving: Make a picture to match the addition problem
Quick Check and Cumulative Review
Chapter Test and Practice game: addition with adding 1
Length of unit: 15 lessons, 3 weeks
Introductory Story: How Many Animals Do You See?
Lesson 1 Demonstrate subtraction with manipulatives, actions and pictures
Lesson 2 Subtract 1 from numbers 1 – 5
Lesson 3 Subtract 1 from numbers 6 – 10
Lesson 4 Writing the number sentence from a picture
Problem Solving: Writing the subtraction sentence from a story
Lesson 6 Subtract 2 from numbers 2 – 5
Lesson 7 Subtract 2 from numbers 6 – 10
Lesson 8 Subtract in vertical form
Lesson 9 Using a picture to write the subtraction problem
Lesson 10 Show that addition and subtraction are opposite operations
Lesson 11 Show subtraction when using pennies to buy objects
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Problem Solving: Decide to add or subtract using a picture/story
Quick Check and Cumulative Review
Chapter Test and Practice game: add numbers and then subtract one
Chapter 9
Geometry and Fractions
Chapter 10
Greater Numbers
Length of unit: 18 lessons, 3 ½ weeks
Introductory Story: Here Comes the Parade
Lesson 1 Recognize and describe circles and squares
Lesson 2 Recognize and describe rectangles and triangles
Lesson 3 Sorting “plane” shapes
Lesson 4 Identify and extend a pattern of “plane” shapes
Quick Check and Cumulative Review
Lesson 5 Introduce 3-D shapes: cone, rectangular prism, cylinder, sphere, cube, pyramid
Lesson 6 Sort 3-D shapes
Lesson 7 Building with 3-D shapes: cylinders, cones, rectangular prisms, cubes
Lesson 8 Recognize that 3-D shapes have surfaces that are “plane” shapes
Problem Solving: counting and comparing “plane” and 3-D shapes
Quick Check and Cumulative Review
Lesson 10 Symmetry
Lesson 11 Using pattern blocks- combining shapes to make new shapes
Lesson 12 Halves
Problem Solving: using pattern blocks to make larger shapes in two different ways
Quick Check and Cumulative Review
Chapter Test and Practice game: practice “plane” and 3-D shapes
Length of unit: 17 lessons, 3 ½ weeks
Introductory Story: At the Seashore
Lesson 1 Identify the teen numbers to 19
Lesson 2 Numbers 10 – 12, using “counting on” from 10
Lesson 3 Numbers 13 – 15, using “counting on” from 10
Lesson 4 Numbers 16 – 19, using “counting on” from 10
Lesson 5 Using dimes and pennies to count to 19
Lesson 6 Order numbers, finding the missing number in the order
Problem Solving: Using a graph to compare data – more than
Lesson 8 Count, identify and write the number 20- using two sets of 10
Lesson 9 Numbers 21 – 25, using two sets of 10 and “counting on”
Lesson 10 Numbers 26 – 30, using two sets of 10 and “counting on” and three sets of 10
Lesson 11 Ordering numbers 0 – 30
Lesson 12 Using a calendar to locate dates using numbers 1 – 31
Lesson 13 Estimating objects of 30 and less
Problem Solving: Estimating groups by: more than, less than or exactly 20
Quick Check and Cumulative Review
Chapter Test and Practice game: numbers to 31 and reinforcing the 10’s
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