Lafayette Parish School System Curriculum Map
Mathematics: Grade 4
Unit 7: Review/Extension of Place Value, Fractions, and More
(LCC Units 7 and 8)
Time frame: 20 School Days
Unit 7 extends students’ understanding of place value by expressing numbers in standard, written, expanded, and verbal forms through 1,000,000. Money,
multiplication and division algorithms, fractions, decimals and percent, as well as algebra are revisited in preparation for fifth grade math. Additionally,
algebra concepts, particularly open/closed and true/false number sentence, and measures of central tendency close out this unit.
Guided Questions
1. Can students tell how the value of a digit changes depending on the digit’s position or place in a number?
2. Can students read and write numbers through 1,000,000 in word, standard, and expanded forms?
3. Can students use objects and pictures to model and interpret models for numbers through 1,000,000?
4. Can students order numbers and use <, >, or = to compare numbers through 1,000,000?
5. Can students use manipulatives to demonstrate that a number is divisible by 2, 3, 5, or 10?
6. Can students interpret the range, mean, median, and mode of a set of data?
7. Can students rewrite products as the sum of two products to illustrate the distributive property of multiplication over addition?
8. Can students read, write, and interpret decimals through hundredths?
9. Can students give and identify the decimal equivalent of halves, fourths, and tenths?
10. Can students use set models, pictures, arrays, and regions to read, write, compare, order, identify, model, and represent fractions through twelfths?
Vocabulary List
Continue to develop previously introduced math vocabulary words in this unit, especially the ones students are having difficulty using correctly.
Teacher
Note
All the GLEs have been taught prior to the LEAP test except taking place value to the millions; open/closed and true/false number sentences;; divisibility; and the
distributive property. You are encouraged to use the rest of the school year to ensure mastery of grade 4 GLEs. Please, remember to include the GLEs in a problemsolving format. This will improve the students’ chances of passing the LEAP should they need to retest this summer.
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
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Lafayette Parish School System Curriculum Map
Mathematics: Grade 4
Unit 7: Review/Extension of Place Value, Fractions, and More
Grade Level Expectations
TLW be able to:
Instructional Notes/Strategies
Basic Facts: —continue daily until mastery
4. Know all basic facts for
multiplication and division
E
through 12 x 12 and 144 
12, and recognize factors of
composite numbers less than
50 [as well as multiples of
natural numbers for 2
through 12] (N1) (N6) (N7)
Resources
 Students should have mastered basic facts by
now. However, please continue to work with
students who have not mastered their facts.
 See instructional notes/strategies from Units
1- 6
 See resources list from Units1-6
Remind students that—
 comparisons are read from left to right. for
example, 612 <6 18 must be read as 612 is
less than 618, rather than 618 is greater than
612.
☛Harcourt— 1.3 (6-9)
Bloom— Knowledge
Focus 7-1: Place Value through 1,000,000 (3 Days)
1.
I
Read and write place value
in word, standard, and
expanded form through
1,000,000 (N1)
Bloom—Comprehension
 associate place value words with how
many digits in a number
 tell how the value of a digit changes
because of its position/place in the
number (tell the value of 5 in 95,836
and 9,577,836)
 read and write in word (six hundred
thirty-two thousand), standard
(632,000), and expanded form
(600,000 + 30,000 + 2,000) through
1,000,000
☛See resources list from Unit 1
 although both statements are correct, remind
students when comparing numbers, it is read
from left to right
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
62
Lafayette Parish School System Curriculum Map
Mathematics: Grade 4
Unit 7: Review/Extension of Place Value, Fractions, and More
Grade Level Expectations
2.
E
Read, write, compare, and
order whole numbers using
place value concepts,
standard notation, and
models through 1,000,000
(N1) (N3) (A1)
TLW be able to:
Instructional Notes/Strategies
 model, compare, and order numbers
☛See instructional notes/strategies from Unit 1
Resources
☛See resources list from Unit 1
through 1,000,000
 interpret models made from place
value blocks and other concert or
pictorial objects
 use < >, or = to compare numbers
Bloom—Application
Focus 7-2: Money, Divisibility, Distributive Property, Multiplication and Division Algorithms (5 Days)
12.
E
Count money, determine
change, and solve simple
word problems involving
money amounts using
decimal notation (N6) (N9)
(M1) (M5)
 count money up to $100
 determine change up to $50
 solve simple word problems using
 See notes from Unit 1
 See resources list from Unit 1
☛ LCC Activities— Unit 1: Activity 3
If You Made a Million
 See notes from Unit 1
 See resources list from Unit 3
decimal notations
Bloom—Application
11.
E
Multiply 3-digit by 1-digit
numbers, 2-digit by 2-digit
numbers, and divide 3-digit
numbers by 1-digit numbers,
with and without remainders
(N6) (N7)
Bloom—Application
 fluently and accurately multiply up to
3-digit numbers by 1-digit numbers
using the distributive property,
standard algorithm, and place value
 fluently and accurately multiply 2-digit
numbers by 2-digit numbers using the
distributive property, standard
algorithm, and place value concept
 fluently and accurately divide 3-digit
numbers by 1-digit numbers with and
without remainders using the standard
algorithm and place value concept
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
63
Lafayette Parish School System Curriculum Map
Mathematics: Grade 4
Unit 7: Review/Extension of Place Value, Fractions, and More
Grade Level Expectations
3.
C
Illustrate with manipulatives
when a number is divisible
by 2, 3, 5, or 10 (N1)
TLW be able to:
Instructional Notes/Strategies
 use objects and pictures to prove that a
number is divisible by 2, 3, 5, and 10
Bloom—Comprehension
17.
C
Use manipulatives to
represent the distributive
property of multiplication
over addition to explain
multiplying numbers (A1)
(A2)
 use manipulatives represent and the
distributive property of multiplication
over addition
 Provide experiences so the students can
discover that will allow them to discover and
make permanent the knowledge that—
♦ numbers are divisible by 2
♦ numbers ending in 0 are divisible by 10
♦ numbers ending in 5 or 0 are divisible
by 5
♦ numbers divisible by 10 are divisible
by 2 and 5
 To distribute something means to hand it out
 Use coins to demonstrate the distributive
property, such as
5 x (2 + 3) = (5 x 2) + (5 x 3)
 Take 25 pennies and make 5 stacks of 2
pennies and 5 stacks of 3 pennies
Bloom—Comprehension
 This represents the right-hand side of the
equation: five times two plus five times three
or written mathematically: (5 x 2) + (5 x 3)
Resources
☛Harcourt— 16.1 ( 336-337)
☛Project Lift —Focus 9, 12, 30, 25
☛Linking Math— A39
☛LCC Activities—See the Activity Alignment
Document for ideas
☛Technology Connection—None Suggested
☛Harcourt— 11.2 ( 238-239); 9.3 ( 188-191)
9.4 ( 192-192)
☛Project Lift —None
☛Linking Math—C3
☛LCC Activities— None Suggested
☛Technology Connection—None Suggested
 Now pair each stack of two pennies with a
stack of three pennies.
 This represents the left side of the example: 5
groups, two plus three in each group [or
written mathematically: 5 x (2 + 3]
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
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Lafayette Parish School System Curriculum Map
Mathematics: Grade 4
Unit 7: Review/Extension of Place Value, Fractions, and More
Grade Level Expectations
TLW be able to:
Instructional Notes/Strategies
Resources
 See instructional notes/strategies from Unit 1
 Finding range and mode are the focus for
fourth grade, however here is where you can
expose them to mean and median.
☛Harcourt—6.2 (119 -121) [Exclude # 8]
6.3 (122-123)
Focus 7-3: Measure of Central Tendency (4 Days)
35
I
Find and interpret the
meaning of [range], mean,
mode, and median of a small
set of numbers using
(concrete objects) when the
answer is a whole number
(D1)
 use manipulatives to determine the
range, mean, mode, and median of a
small set of objects
☛LEAP Tutoring Guide—Pages 110B-113B
☛Technology—
Focus 7-4: True or False, Open or Closed Number Sentences, and One-Step Equations (4 Days)
18. Identify and create true/false  create and identify true and false 
C
number sentences
and open/closed number
sentences (A2)
 create and identify open and closed
number sentences
Bloom—Synthesis
Solve one-step equations
with whole number solutions
(A2) (N4)
☛Linking Math—A 40
☛LCC Activities— Unit 7: Activity 10:
Mouth-watering Math) and Unit 8: Activity
11 (What Does This Mean?)
Bloom—Application
19.
C
☛Project Lift—Focus 24/28
 solve one-step equations involving
addition, subtraction, and basic fact
multiplication and division
 See instructional notes/strategies from Unit 2
☛Harcourt—none
☛Project Lift—Focus7
☛Linking Math—none
☛LCC Activities— Unit 5: Activity 12 (True
or False)
☛LEAP Tutoring Guide—Pages 14A-17A
☛Technology—None Suggested
 See notes from Unit 1
☛LCC Activities— Unit 8: Activity 3 (Guess
Your Number)
Bloom-- Application
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
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Lafayette Parish School System Curriculum Map
Mathematics: Grade 4
Unit 7: Review/Extension of Place Value, Fractions, and More
Grade Level Expectations
TLW be able to:
Instructional Notes/Strategies
Resources
Focus 7-5: Model, Read, Write, Compare, Order, and Represent Fractions, Decimals, and Percent (4 Days)
6.
E
Model, read, write, compare,
order, and represent
fractions with denominators
through twelfths using
region and set models (N1)
(A1)
 represent fractions that have
denominators of 2 through 12 as parts
of a whole, parts of a set, and points
on the number line
 model, read, write, compare, and
order fractions that have
denominators of 2 through 12
 See instructional notes/strategies from Unit 6
 See resources list from Unit 6
 use pictures, models, and diagrams to
 See instructional notes/strategies from Unit 6
 See resources list from Unit 6
 See instructional notes/strategies from Unit 6
 See resources list from Unit 6
 See instructional notes/strategies from Unit 6
 See resources list from Unit 6
☛LCC Activities— Activity 2 (Ordering
Decimals)
Bloom—Application
9.
I
Estimate fractional amounts
through twelfths, using
pictures, models, and
diagrams (N2)
Bloom—Application
5.
I
Read, write, and relate
decimals through
hundredths and connect
them with corresponding
decimal fractions (N1)
estimate fractional amounts
 use models or pictures to identify
equivalent fractions and to compare
and order them
 read and write decimals through
hundredths as fractions
 change and discuss common
benchmark fraction to decimals, and
vice versa
Bloom—Comprehension
7.
C
Give decimal equivalents of
halves, fourths, and tenths
(N2) (N1)
Bloom—Comprehension
 use models to show the decimal
equivalents for halves, fourths, and
tenths
 write fractions, decimals, and percents
that name the same number, especially
for halves, fourths, and tenths
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
☛LCC Activities—Activity 6
(Fraction/Decimal/Percent Dominoes) and
Activity 7(Professor Know-it-All)
66
ACTIVITIES
FOR YOUR CONSIDERATION
Activity 2: Ordering Decimals (GLEs: 5, 6)
Materials List: zip-lock bags, plastic coins, index cards with decimals written on them, pencil
Give each student the following money amounts and have them put them in order by value, starting with the smallest amount (10¢, 25¢, 75¢, 5¢, 50¢, 1¢, $1.00). Help them
connect these amounts to the corresponding equivalent decimal by putting the decimal amounts under each money amount. Discuss how decimals are ordered. Explain the
place value of decimals to the hundredths place. Next, explain that a decimal is another way of writing a fraction. Have the students state the equivalent fraction for given
decimal amounts. Record their responses on the board. (.01 = 1/100, .05 = 5/100 or 1/20, .10 = 10/100 or 1/10, .25 = 25/100 or 1/4, .50 = 50/100 or 1/2, .75 = 75/100 or 3/4)
Working in pairs, give students a zip-lock bag with three to four cards in it with a decimal amount on each card and its equivalent fraction. Have the students take out the
cards and put them in order. Allow them to use their plastic coins if needed. Check for accuracy. Have students exchange bags and repeat the activity.
Activity 3: If You Made a Million! (GLEs: 2, 4, 12, 14) *From Unit 1
Materials List: resources to find costs of items, (newspapers, magazines, or Internet access), calculator, pencil, paper, If You Made a Million by David M. Schwartz
(optional)
Students will create a story chain (view literacy strategy descriptions). Story chains are especially useful in teaching math concepts, while at the same time promoting
writing and reading. Students can be creative and use information and math from their everyday life. To create this story chain, put students in groups of four. On a sheet of
paper, ask the first student to write the opening sentence of the Math Chain Story, “If I had a Million Dollars I would...”
(The first student will put what they would do
or buy and how much it would cost.) The second student would use the calculator and subtract that amount. Next, he/she would continue the story by adding what they
would do/buy. The third and fourth persons would do the same. They will continue in this manner until there is no more money. The students may use newspapers,
magazines, or the computer to find the costs of different items they would buy “if they made a million.”
Optional: Read and discuss the book, If You Made a Million by David M. Schwartz. (This book describes the various forms money can take, including coins, paper money
and personal checks and how money can be used to make purchases pay off loans, or build interest in a bank.)
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Activity 6: Fraction/Decimal/Percent Dominoes (GLEs: 6, 7, 9)
Materials List: Fraction/Decimal/Percent Dominoes BLM, card stock
Make a set of fraction/decimal/percent domino cards by running the Fraction/Decimal/Percent BLM on card stock. Run enough copies for students to work in pairs. Place
all dominoes face down. Have each player choose three dominoes. Taking turns,
have players place dominoes against other dominoes with equal value. If a player cannot make a play, he or she draws a domino from the pile until a play is possible. Play
continues until one player has no more dominoes or until no more plays can be made.
Activity 7: Professor Know-It-All (GLEs: 5, 7, 9)
Materials list: index cards, pencils
Students will work in groups of threes. They will choose a fraction through twelfths and record the fraction and its corresponding decimal and percent on an index card to
be used to play professor know-it-all (view literacy strategy descriptions). One group will come to the front of the room and take on the role of “Professor.” Another group
will read their fraction, decimal or percent. The Professor” group will have to state the two missing parts. Rotate groups of know-it-alls after 5 minutes to include all groups.
Example: Group 1 has written
Group 1 says, “75%.”
Group 2 “The Professor” responds, ¾ and .75.
Activity 10: Mouth-watering Math (GLEs: 5, 6, 7, 8, 9, 35, 36, 41)
Materials List: color coated candy, crayons, paper, pencil
Show students a spoonful of colored coated candy such as mini M&Ms®. Have them write down their estimate of the amount of candy in the spoon. Then have the class
create a line plot of their estimates on the board. Discuss mean, mode, and median of the estimated data. Count candies to find the actual number of candies in the spoon.
Make a new line plot with the actual data. Find the mean, mode, and median for the new data. Compare the estimated and actual data.
Next, give each pair of students a small bag of the color coated candy and ask them to estimate the amount of candy in the bag, using the spoonful of candy as their
benchmark. After recording their estimates, have them count the candy, record the actual amount of candy in the bag, and find the difference between their estimates and
the actual amount. Have students classify the candy by color, record the fractional part of each color, and list the fractions in order from the least to the greatest. Have
students construct a pie (circle) graph using 25 of the candies. Have them put the candies together in the circle by color. Make a legend showing that for this graph1 candy =
4% candies since a pie graph represents 100%. Then have each pair of students record the pie graph on a sheet of paper using the corresponding crayon that matches the
candy. Have them draw the appropriate lines on the pie graph where one color begins. Have them write in each fractional part of the graph along with the corresponding
decimal and percent amounts. Have them check that their graph contains all necessary parts-title, labels, scale, legend. Discuss why this type of graph is good to use when
you are showing parts of a whole. Discuss other times a pie graph may be used. Have them write probability statements about each color of candy based on their graph.
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
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Activity 11: What Does This Mean? (GLE: 35) *From Unit 8
Materials List: connecting cubes, paper, pencil
Students are presented with five stacks of connecting cubes, two stacks that are 3 cubes high, one 6 cubes high, and two 4 cubes high. Ask students to determine the mode
height, the median height, and the mean height for this set of data. Students will determine the mode by grouping the stacks according to height. The stacks with the same
number of cubes in it that appears most often is the mode. Students will determine the median by putting the stacks in order from shortest to longest and then selecting the
stack in the middle. (Keeping the number of stacks odd facilitates getting a whole number median.) Students will determine the mean by “leveling” the stacks. In this case,
they could make all the stacks have 4 cubes. Allow the students to make up their own problems, using the cubes. Make sure students state the mean, mode, and median for
each set of cubes they use.
Activity 12: True or False (GLE: 4, 18)
Materials List: paper, pencil, teacher-made cards with division sentences, extra index cards
In preparation for the True or False game, have the students create a Divisibility Rules word grid (view literacy strategy descriptions). This activity will help students
review the important concepts of the divisibility rules. It will also serve to reinforce prime and composite numbers. Have students generate three or four digit numbers to
use for the word grid. Through student participation, fill in the word grid by placing “+” in the space of any divisibility rule that applies for that number and determine if
that number is prime or composite.
 Next have the students work with a partner. Give one card from the set of cards with division sentences you created to each group. Students, working with
a partner, read the sentence, then rewrite the sentence using math symbols when possible, state if the number sentence is true or false, and explain their
reasoning. These activities should involve estimations where students have to determine if the estimation is appropriate and give a rationale for why or
why not.
LPSS Comprehensive Curriculum 2011-2012
Grade 4: Mathematics Unit 7
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Examples of cards could include:
• 57 divided by 4 is less than 57 The group writes 57 ÷ 4 < 57 The number sentence is true because when you divide 57 into 4 groups no group can have
all 57 in it.
• The remainder when 545 divided by 5 results in 5. The group writes 545 ÷ 5 =N with a remainder of 5 is not true because if you have 5 left you can
divide the number one more time. (Or it is not true because 545 is a multiple of 5 so 545 can be evenly divided by 5. There would be no remainder.)
• 9,578 is divisible by 2.
• 2,467 is divisible by 2.
• 578 divided by 8 is greater than 586 divided by 8.
• 9 divided by 0 is 9.
When students have completed these cards, they could make up a similar set of cards to exchange with another group and repeat the process. When the
sets are completed, they would be returned to the original group to check.
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Grade 4: Mathematics Unit 7
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