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Getting Started
Math Message • Self Assessment
Home Link 8 8 Follow-Up
Complete the Self Assessment (Assessment
Handbook, page 182).
Review answers. Have children share strategies
for solving the problems.
䉬
Assessment Master
Name
1 Assessing Progress
Date
Time
Self Assessment
LESSON
89
䉬
Progress
Check 8
Check one box for each skill.
䉴 Math Message Follow-Up
INDEPENDENT
ACTIVITY
(Self Assessment, Assessment Handbook, p. 182)
Skills
I can do this on
my own and can
explain how to do it.
I can do
this on
my own.
I can do this if I
get help or look
at an example.
1. Read and write
fractions.
The Self Assessment offers children the opportunity to
reflect upon their progress.
2. Compare fractions
to 12.
3. Find fractional parts
of collections.
䉴 Oral and Slate Assessments
WHOLE-CLASS
ACTIVITY
Problems 1, 3, and 4 provide summative information that can be
used for grading purposes. Problem 2 provides formative
information that can be useful in planning future instruction.
Oral Assessment
1
1. Tell whether each fraction is greater than ᎏ2ᎏ (show thumbs up),
1
1
less than ᎏ2ᎏ (show thumbs down), or equal to ᎏ2ᎏ (show fist with
thumb tucked in).
2
1
3
7
1
4. Write fractions on a
number line.
5. Complete a
symmetrical shape.
6. Tell the value of each
digit in a decimal.
Assessment Handbook, p. 182
4
Suggestions: ᎏ4ᎏ fist; ᎏ3ᎏ down; ᎏ4ᎏ up; ᎏ8ᎏ up; ᎏ4ᎏ down; ᎏ8ᎏ fist
2. Identify the value of digits in 3-place decimals. Be sure to
include numbers with zeros. For example, write 3.087 on the
board. Ask children to identify the value of each digit. 3 means
3 ones; 0 means 0 tenths; 8 means 8 hundredths; 7 means
7 thousandths
Slate Assessment
3. Divide the slate into fractions of a region. Shade a specified
2
fraction. Suggestions: Divide into halves and shade ᎏ2ᎏ; divide
3
2
into fourths and shade ᎏ4ᎏ; divide into thirds and shade ᎏ3ᎏ;
5
divide into eighths and shade ᎏ8ᎏ.
4. Tell fraction number stories. Encourage children to use
counters, arrays, or diagrams to help them solve the problems.
●
●
●
Cora had 5 friends over for pizza. The 6 shared 1 pizza
1
equally. What fraction of the pizza did each person receive? ᎏ6ᎏ
1
ᎏᎏ
2
Manuel had a bag of 12 marbles. He lost of the marbles.
How many marbles did he lose? 6 marbles
1
ᎏᎏ
4
Another day, Manuel had 16 marbles. He lost of the
marbles. How many marbles did he lose? 4 marbles
Assessment Master
Name
Date
Time
Written Assessment
LESSON
89
䉬
Progress
Check 8
Part A
Use counters to help.
1. Circle
7
8
2. Shade
of the marbles.
3. Write at least 5 names in this
name-collection box.
of the squares.
4. Write the missing fractions
on the number line.
Sample answers:
1
2
0
6
12
2
4
2
3
1 12
1
4
1
2
3
4
1
or
2
4
one-half
5. Circle all the fractions below that are greater than 12. Use your Fraction
Cards to help.
7
8
1
3
1
4
3
8
2
4
6. In the number 28.47
the 2 means
the 8 means
the 4 means
the 7 means
2 tens
8 ones
4 tenths
7 hundredths
2
3
3
4
7. If I wanted an equal chance of
taking out a sphere or a cube
I would put in 2 spheres.
Assessment Handbook, p. 183
Lesson 8 9
䉬
695
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Assessment Master
Name
Date
LESSON
䉴 Written Assessment
Time
Written Assessment continued
8䉬 9
INDEPENDENT
ACTIVITY
(Assessment Handbook, pp. 183–185)
Solve. Draw a picture to show what you did.
Four people share 8 pieces of candy.
2
8. a. How many pieces does each person get?
pieces
1
ᎏᎏ
4
b. What fraction of the candy did each person get?
9. Fill in the blanks.
120 minutes =
1
2
30 minutes =
1
ᎏᎏ
2
60 minutes =
15
Part A
2
8
or ᎏᎏ
10. Use a straightedge. Draw the
other half of the symmetric
shape.
hour
Recognizing Student Achievement
Problems 1⫺10 provide summative information that can be used
for grading purposes.
Problem(s)
Description
1, 2, 8b
Find fractional parts of sets.
3
Write equivalent names for ᎏ2ᎏ.
4
Write fractions in order.
5
Compare fractions to ᎏ2ᎏ.
6
Identify the value of digits in decimals.
7
Predict outcomes of simple experiments.
8a
Use equal sharing to demonstrate the meaning
of division.
9
Describe relationships among units of time.
10
Complete a 2-dimensional symmetric design.
hours
hour
1
4
minutes = ᎏᎏ hour
1
Part B
Shade the circles to match the mixed number or fraction.
11.
9
5
Write another name for 9 .
5
1ᎏ45ᎏ
12.
23
Write another name for 2 34 .
4
11
ᎏᎏ
4
1
Assessment Handbook, p. 184
Part B
Informing Instruction
Problems 11⫺16 provide formative information that can be useful
in planning future instruction.
Assessment Master
Name
Date
LESSON
13. Cross out all the names that do
not belong in this name-collection
box. Then add one more name.
14. Fill in the blanks.
Use a clock
to help.
11
10
12
1
2
9
3
8
6
8
1
4
4
7
6
5
1
8
12
90 minutes =
75
20
1
two-fourths
three-thirds
three-fourths
1ᎏ2ᎏ
hours
minutes = 1ᎏ14ᎏ hours
1
3
1
60
minutes = ᎏᎏ hour
minute = ᎏᎏ hour
5 minutes =
1
ᎏᎏ
12
hour
Solve. Use coins to help.
15. Lora’s mom gave her
3
ᎏᎏ
4
Greg’s mom gave him
of a dollar to buy a drink.
4
ᎏᎏ
5
of a dollar to buy a drink.
Who received more money?
Greg
Three-fourths of a dollar is
of a dollar is $0.80.
Explain how you got your answer.
$0.75, and
4
ᎏᎏ
5
16. If I wanted to take out a sphere about half as often as a cube, I would put
in
2
spheres.
Assessment Handbook, p. 185
696
11, 12
Shade circles to match mixed numbers or
fractions.
13
Find equivalent names.
14
Describe relationships among units of time.
15
Solve a problem involving fractional parts of
collections.
16
Predict outcomes of an experiment.
Time
Sample answer:
5
10
Description
Written Assessment continued
8䉬 9
3
ᎏᎏ
4
Problem(s)
Unit 8 Progress Check 8
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Assessment Master
䉴 Open Response
INDEPENDENT
ACTIVITY
(Assessment Handbook, p. 186)
Name
Date
Time
Open Response
LESSON
89
䉬
Progress
Check 8
Solving a Coin Problem
Robert found 24 coins. 13 of them were pennies, 14 of them were nickels,
1
of them were dimes, and the rest were quarters.
6
Solving a Coin Problem
The open response item requires children to apply skills and
concepts from Unit 8 to solve a multistep problem. See the
Assessment Handbook, pages 113–117 for rubrics and children’s
work samples for this problem.
1. Tell how many of each coin Robert found. Show all of your work. Use
coins, pictures, counters, or whatever you need.
8
4
Robert had
6
6
pennies
dimes
nickels
quarters
2. Explain how you found the number of dimes.
2 Building Background for Unit 9
䉴Math Boxes 8 9
3. How much are his coins worth altogether?
Show all of your work.
$2.28
INDEPENDENT
ACTIVITY
䉬
(Math Journal 2, p. 203)
Mixed Practice This Math Boxes page previews Unit 9
content.
䉴 Home Link 8 9:
Assessment Handbook, p. 186
INDEPENDENT
ACTIVITY
䉬
Unit 9 Family Letter
(Math Masters, pp. 263ⴚ266)
Home Connection The Unit 9 Family Letter provides
parents and guardians with information and activities
related to Unit 9 topics.
Student Page
Home Link Masters
Name
HOME LINK
89
䉬
Date
Time
Date
Unit 9: Family Letter
89
䉬
Multiplication and Division
1.
In Unit 9, children will develop a variety of strategies for multiplying whole numbers.
They will begin by using mental math (computation done by counting fingers, drawing
pictures, making diagrams, and computing in one’s head). Later in this unit, children
will be introduced to two specific algorithms, or methods, for multiplication: the
partial-products algorithm and the lattice method.
28
4
Multiply 4 20.
Multiply 4 8.
Add the two partial products.
∑
∑
∑
80
32
112
First, calculate 4 [20s].
Then calculate 4 [8s].
Finally, add the two partial products.
It is important that when children verbalize this method, they understand and say
4 [20s], not 4 2. In doing so, they gain a better understanding of the magnitude of
numbers along with better number sense.
379
4
Multiply 4 300.
Multiply 4 70.
Multiply 4 9.
∑
∑
∑
∑
1,200
280
36
First, calculate 4 [300s].
Second, calculate 4 [70s].
1,516
Then calculate 4 [9s].
Finally, add the three partial products.
Check that when your child is verbalizing this strategy, he or she says 4 [300s], not
4 3; and 4 [70s], not 4 7. Using this strategy will also help to reinforce your child’s
facility with the basic multiplication facts and their extensions.
Math Masters, pp. 263–266
Solve.
2.
42
420
4,200
7 60 7 600 ⴜ
ⴛ
ⴜ
ⴛⴛ ⴛ
ⴜ ⴜ
Add the three partial products.
Math Boxes
76
Partial-Products Algorithm
The partial-products algorithm is a variation of the traditional multiplication algorithm
that most adults learned as children. Note that the multiplication is done from left to
right and emphasizes place value in the numbers being multiplied.
Time
LESSON
48
480
4,800
3.
Each person gets $
500 is
as 5.
0.90
.
Share $9 equally among 4 people.
Each person gets $
86
2.25
.
8 60
8 600
30 is 10 times as much as
3
Share $2.70 equally among
3 people.
4.
.
100
6 coats. 4 buttons per coat.
How many buttons in all?
24
times as much
buttons
Write a number model.
8,000
6 4 24
is 100 times as much
as 80.
40,000 is 1,000 times as much
as
5.
40
.
Draw a 4-by-7 array of Xs.
6.
18 books. 6 books per shelf.
How many shelves?
3
How many books left over?
How many Xs in all?
28
3
Write a number model.
4 7 28
0
4 children share 13 marbles.
How many marbles per child?
How many marbles left over?
64 65
1
Math Journal 2, p. 203
Lesson 8 9
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697