www.everydaymathonline.com eToolkit ePresentations Interactive Teacher’s Lesson Guide Algorithms Practice EM Facts Workshop Game™ Assessment Management Family Letters Curriculum Focal Points Common Core State Standards 384 Unit 6 Whole-Number Operations and Number Stories Advance Preparation For the Solving Comparison Number Stories activity in Part 1, decide how you will display a comparison diagram. Some possibilities: • Make an overhead transparency of Math Masters, page 436. • Draw and erase comparison diagrams on the board as needed. Teacher’s Reference Manual, Grades 1–3 pp. 84–94, 225–227 Comparison Number Stories Objective To introduce comparison number stories by using comparison diagrams. c Key Concepts and Skills • Share number story solution strategies. [Operations and Computation Goal 2] • Describe and solve comparison number stories. [Operations and Computation Goal 4] • Write number models to summarize addition and subtraction number stories. [Patterns, Functions, and Algebra Goal 2] Key Activities Children are introduced to the comparison diagram as a tool for recording known and missing information in a comparison number story. Children then solve comparison number stories by using comparison diagrams and writing number models. Ongoing Assessment: Informing Instruction See page 387. Ongoing Assessment: Recognizing Student Achievement Use journal page 134. [Operations and Computation Goal 4] Key Vocabulary comparison number story difference comparison diagram Materials Math Journal 1, pp. 134 and 135 My Reference Book, pp. 110 and 111 Home Link 6 1 transparency of Math Masters, p. 436 (optional) number line number grid (optional) Playing Addition Top-It My Reference Book, pp. 122 and 123 Math Masters, pp. 449 and 473 (optional) per partnership: 4 each of number cards 0–20 (from the Everything Math Deck, if available) Children practice adding three or more numbers. Math Boxes 6 2 Math Journal 1, p. 136 Children practice and maintain skills through Math Box problems. Home Link 6 2 Math Masters, pp. 159 and 160 Children practice and maintain skills through Home Link activities. READINESS Doing a Penny Grab Activity 30 pennies or other small counters Children compare numbers using a concrete model. ENRICHMENT Comparing Number Stories Math Masters, p. 161 Children compare two number stories by writing number models and answering related questions. Teaching the Lesson Ongoing Learning & Practice 1 3 2 4 Differentiation Options
Transcript
www.everydaymathonline.com
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshopGame™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
384 Unit 6 Whole-Number Operations and Number Stories
Advance PreparationFor the Solving Comparison Number Stories activity in Part 1, decide how you will display a comparison
diagram. Some possibilities:
• Make an overhead transparency of Math Masters, page 436.
• Draw and erase comparison diagrams on the board as needed.
Teacher’s Reference Manual, Grades 1–3 pp. 84–94, 225–227
ComparisonNumber Stories
Objective To introduce comparison number stories by using
comparison diagrams.c
Key Concepts and Skills• Share number story solution strategies.
[Operations and Computation Goal 2]
• Describe and solve comparison number
stories. [Operations and Computation Goal 4]
• Write number models to summarize
addition and subtraction number stories.
[Patterns, Functions, and Algebra Goal 2]
Key ActivitiesChildren are introduced to the comparison
diagram as a tool for recording known and
missing information in a comparison number
story. Children then solve comparison
number stories by using comparison
diagrams and writing number models.
Ongoing Assessment: Informing Instruction See page 387.
Ongoing Assessment: Recognizing Student Achievement Use journal page 134. [Operations and Computation Goal 4]
Key Vocabularycomparison number story � difference �
comparison diagram
MaterialsMath Journal 1, pp. 134 and 135
My Reference Book, pp. 110 and 111
Home Link 6�1
transparency of Math Masters, p. 436
(optional) � number line � number grid
(optional)
Playing Addition Top-ItMy Reference Book, pp. 122 and 123
Math Masters, pp. 449 and 473
(optional)
per partnership: 4 each of number
cards 0–20 (from the Everything Math
Deck, if available)
Children practice adding three or
more numbers.
Math Boxes 6�2Math Journal 1, p. 136
Children practice and maintain skills
through Math Box problems.
Home Link 6�2Math Masters, pp. 159 and 160
Children practice and maintain skills
through Home Link activities.
READINESS
Doing a Penny Grab Activity30 pennies or other small counters
Children compare numbers using a
concrete model.
ENRICHMENTComparing Number StoriesMath Masters, p. 161
Algebraic Thinking Use the Math Message problem to start a discussion of comparison number stories. Comparison stories involve the difference between two quantities. The Math Message number story compares two things that are measured.
You can also compare things that are counted.
Example:
� Beth scored 14 points. Ivy scored 8 points. So Beth scored 6 more points than Ivy. (Alternately, Ivy scored 6 fewer points than Beth.) The difference in points scored is 6 points.
Draw a picture on the board and show how children can solve the Math Message problem by matching the two quantities one to one. (See margin.) Discuss the meaning of the word quantity in the diagram. The quantity that is left unmatched is the difference. In the Math Message problem, the difference tells how many more inches Fish A is than Fish B.
Display a transparency of a comparison diagram (Math Masters, page 436) or draw one on the board. In it, write the numbers 14, 6, and 8. (See margin.) Say that the diagram is a convenient way to represent the fish comparison story. The longer Quantity cell shows the larger number of inches of Fish A. The shorter Quantity cell shows the smaller number of inches of Fish B. The Difference cell shows how many more inches Fish A is than Fish B.
Getting Started
Math Message Fish A is 14 inches long. Fish B is 6 inches long.
How many more inches long is Fish A than Fish B?
8 inches
Home Link 6�1 Follow-Up Ask volunteers to share how they found the answer to each problem and why they chose the order in which they added the three numbers.
Mental Math and Reflexes Write multiple-addend problems like the following on the board. Encourage children to look for combinations that will make the addition easier.
386 Unit 6 Whole-Number Operations and Number Stories
Quantity
Difference
Quantity
30 Joey
10 Max ?
Quantity
Difference
Quantity
$47 radio
$20 watch ?
Quantity
Difference
Quantity
$47 radio
? calculator $12
Adjusting the Activity Whenever a comparison diagram is
provided, children should always write the
known and missing information (shown with
a question mark) on the diagram. Have
children write words or short phrases on the
diagram as a reminder of what the numbers
mean. For the Math Message problem, the
words “Fish A” and “Fish B” might be written
as reminders.
AUDITORY � KINESTHETIC � TACTILE � VISUAL
Write a number model that represents the problem using a question mark to represent what children have to find out to solve the problem (or what they don’t know). Tell them that the number story might be modeled using any of four possible number models. The choice of a number model depends on how a child thinks about the problem. Write the remaining number models below the diagram (in all, 14 – 6 = ?, 14 – ? = 8, ? + 6 = 14, and 6 + ? = 14). Then, below the open sentences, write number models for the solution to the problem with 8 substituted for the question mark.
� Solving Comparison WHOLE-CLASS ACTIVITY
Number Stories(My Reference Book, pp. 110 and 111)
Algebraic Thinking You may wish to read about comparison diagrams in My Reference Book, pages 110 and 111 with your class. Display a comparison diagram. Work with the children to solve several comparison stories.
Example 1
Joey scored 30 points. Max scored 10 points. How many more points did Joey score than Max? 20 points
Fill in the comparison diagram as shown in the margin. Write ? for the difference, which is the number to be found. Invite children to share mental-arithmetic strategies for finding the difference between 30 and 10. Sample strategies:
� Think, “What must I add to 10 to get 30?”
� Think of the comparison diagram as a Fact Triangle. Think, “30 - 10 is the difference I want.”
As children share their solution strategies, write a number model below the diagram to represent one of the strategies using ? for the unknown number. Then, below the open sentence, write a number model for the solution to the problem with 20 substituted for the question mark. For example, for the first strategy, write 10 + ? = 30 and 10 + 20 = 30.
Example 2
A radio costs $47. A watch costs $20. How much more does the radio cost? $27
This problem is similar to the previous example. With the class, fill in the comparison diagram as shown in the margin. Invite children to share their strategies for solving the problem.
As children share their solution strategies, write a number model below the diagram to represent one of the strategies using ? for the unknown number. Then, below the open sentence, write a number model for the solution to the problem with $27 substituted for the question mark.
Example 3
A radio costs $47. A calculator costs $12 less than the radio. How much does the calculator cost? $35 Fill in the diagram as shown in the margin.
� Write the numbers you know in the comparison diagram.
� Write ? for the number you want to find.
� Solve the problem.
� Write a number model.
1. Barb scored 27 points. Cindy scored 10 points.
Barb scored more points than Cindy.
Number model:
2. Frisky lives on the 16th floor. Fido lives on the 7th floor.
Frisky lives floors higher than Fido.
Number model:
3. Ida is 36 years old. Bob is 20 years old.
Ida is years older than Bob.
Number model:
Quantity
Quantity
Difference
Quantity
Quantity
Difference
Quantity
Quantity
Difference
�
�
Number models vary.
27
16
36
10 ?
?
?
7
20
27 - 10 = 17
16 - 7 = 9
36 - 20 = 16
17
9
16
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Math Journal 1, p. 134
Student Page
Comparison Number Stories continuedLESSON
6 �2
Date Time
4. A jacket costs $75. Pants cost $20.
The pants cost $ less than the jacket.
Number model:
5. Jack scored 13 points. Jack scored 6more points than Eli.
Eli scored points.
Number model: or 6. Billy is 16 years old. Paul is
6 years younger than Billy.
Paul is years old.
Number model: or 7. Marcie is 56 inches tall.
Nick is 70 inches tall.
Marcie is inches shorter than Nick.
Number model:
or
Quantity
Quantity
Difference
Quantity
Quantity
Difference
Quantity
Quantity
Difference
Quantity
Quantity
Difference
Try This
?
?
6
6
75 - 20 = 55
7 + 6 = 1313 - 6 = 7
6 + 10 = 1616 - 6 = 10
55
7
10
14
75
20
?
16
?
70
56
13
56 + 14 = 7070 - 56 = 14
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Math Journal 1, p. 135
Student Page
Lesson 6�2 387
This example differs from the previous ones—this time, the smaller quantity is not known, but the difference is known. Make sure that children understand this. The strategies for solving this problem are the same as before, except that counting up is replaced by counting back (start at 47, count back 12).
� Solving Comparison PARTNER ACTIVITY
Number Stories(Math Journal 1, pp. 134 and 135)
Algebraic Thinking Partners complete the problems on the journal pages. Check that children are recording the known information in the comparison diagram and that they are writing a question mark to represent the unknown number. For most problems, the difference will be the unknown number. For some problems, however, the difference will be known, and one of the two quantities will be unknown.
Ongoing Assessment: Journal page 134
Problems 1
and 2 �Recognizing Student Achievement
Use journal page 134, Problems 1 and 2 to assess children’s ability to solve
comparison number stories. Children are making adequate progress if they can
solve the problems using the number grid, number line, drawings, or manipulatives.
Some children may be able to write a number model that summarizes the problem.
Others may be able to do Problems 5, 6, and 7 with an unknown quantity.
[Operations and Computation Goal 4]
Ongoing Assessment: Informing Instruction
Watch for children who have difficulty writing a number model; have them think
of 17, 8, and 9 as the numbers on a Fact Triangle. Ask them what addition and
subtraction sentences they can make using the three numbers.
Children may use number lines, number grids, or any other learning tool. It is fine for children to draw pictures and doodles.
2 Ongoing Learning & Practice
� Playing Addition Top-It PARTNER ACTIVITY
(My Reference Book, pp. 122 and 123;
Math Masters, p. 449)
Addition Top-It was introduced in Lesson 1-4 to practice facts and compare sums. A domino version was played in Lesson 2-5. An optional record sheet can be found on Math Masters, page 449.
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388 Unit 6 Whole-Number Operations and Number Stories
17 19
10 8 13 11
14 16
�5�2
Math BoxesLESSON
6 �2
Date Time
1. Fill in the frames.
3. Write �, �, or �.
7 � 5 � 30 40
11 � 6 � 4 26
32 18 � 7 � 2
19 13 � 9 � 1�
�
�
�
6. Halve.
2 10
4 14
8 50 2547251
2. Draw all the possible ways toshow 30¢ using ‰, Í, Â.
‰ÂÍÍÍÍÍÂÂÍÂÂÂÂÂÂÂÂÂÂ
4. Draw a line segment that isabout 5 cm long.
5. Write the time.
: 257
12 12
3
4567
8
9
1011
Unit
9
98 99
Math Journal 1, p. 136
Student Page
Name Date Time
Today your child learned about a device that is useful when solving number stories. Wecall it a comparison diagram. Diagrams like these can help your child organize theinformation in a problem. When the information is organized, it is easier to decide whichoperation (�, �, �, or �) to use to solve the problem.
Comparison diagrams are used to represent problems in which two quantities are given andthe question is how much more or less one quantity is than the other (the difference).
Example 1: There are 49 fourth gradersand 38 third graders. How many more fourthgraders are there than third graders?
Note that the number of fourth graders isbeing compared with the number of thirdgraders.
• Answer: There are 11 more fourth gradersthan third graders.
• Possible number models: Children who thinkof the problem in terms of subtractionwill write 49 � 38 � 11. Other childrenmay think of the problem in terms ofaddition: “Which number added to 38will give me 49?” They will write thenumber model as 38 � 11 � 49.
Example 2: There are 53 second graders.There are 10 more second graders thanfirst graders. How many first graders are there?
Note that sometimes the difference is knownand that one of the two quantities is unknown.
• Answer: There are 43 first graders.
• Possible number models: 53 � 10 � 43 or 10 � 43 � 53
For Problems 1 and 2, ask your child to explain the number model that he or she wrote.Also ask your child to explain the steps needed to solve Problems 4–6.
Please return the second page of this Home Link to school tomorrow.
pyg
gp
HOME LINK
6�2 Comparison Number Stories
Quantity
Quantity
Difference
49 fourth graders
38 thirdgraders ?
Quantity
Quantity
Difference
53
? 10
Your child may write words in the diagramas a reminder of what the numbers mean.
110 111
FamilyNote
Math Masters, p. 159
Home Link Master
Add. Use the partial-sums method.
4. 5. 6. 80� 787
33� 5487
40� 1555
48� 755
90� 11
39� 62
Name Date Time
HOME LINK
6�2 Comparison Stories continued
In each number story:
� Write the numbers you know in the comparison diagram.
� Write ? for the number you want to find.
� Solve the problem. Then write a number model.
1. Ross has $29. Omeida has $10.
Ross has $ more than Omeida.
Number model:
2. Omar swam 35 laps in the pool. Anthony swam 20 laps.
Anthony swam fewer laps than Omar.
Number model:
3. Claudia’s birthday is June 10. Tisha’s birthday is 12 days later.
Tisha’s birthday is June .
Number model: 10 � 12 � 2222
20 � 15 � 35
15
29 � 10 � 1919
Sample numbermodels are given.
Quantity
Quantity
Difference
29
10 ?
Quantity
Quantity
Difference
35
20 ?
Quantity
Quantity
Difference
?
10 12
Practice Unit
101 101Math Masters, p. 160
Home Link Master
Children now play another version with number cards 0 through 20. They draw 3 or 4 cards at each turn to practice addition with 3 or 4 numbers.
NOTE Some children may prefer to play Three Addends from Lesson 6-1 again.
Math Masters, page 473 is available for children to record their numbers and
number models.
� Math Boxes 6�2 INDEPENDENTACTIVITY
(Math Journal 1, p. 136)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-4. The skill in Problem 6 previews Unit 7 content.
Writing/Reasoning Have children draw, write, or verbalize their answers to the following: Explain how you know you have written all the possible coin combinations
for 30¢ in Problem 2. Sample answer: I started with a quarter and a nickel. I then used 3 dimes to make 30¢ and then I kept breaking the dimes into 2 nickels until I used all nickels. This is the smallest coin I could use.
� Home Link 6�2 INDEPENDENTACTIVITY
(Math Masters, pp. 159 and 160)
Home Connection Children solve comparison number stories. They fill in a comparison diagram and write a number model for each problem. The explanation in the
Family Note will help parents and guardians feel comfortable when participating in these activities with their children.
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Solve each number story. Be sure to write a number model.Then answer the questions at the bottom of the page.
1. There were 23 children in the classroom. 17 went to the computer lab. How many were left in the classroom?
Number Model:
2. There were 6 children in the classroom. 17 came back from the computer lab. How many children are in the classroom now?
Number Model:
How are the problems alike?
How might solving Problem 1 help you solve Problem 2?Explain your thinking.
will go together in an addition problem.problem, then they are a fact family andthree numbers go together in a subtractionSample answer: If you know that the
3 numbers.Sample answer: They use the same
6 � 17 � 23
23 � 17 � 6
LESSON
6�2
Name Date Time
Comparing Number Stories
Math Masters, p. 161
Teaching Master
Lesson 6�2 389
3 Differentiation Options
READINESS PARTNER ACTIVITY
� Doing a Penny Grab Activity 5–15 Min
To provide experience with comparing numbers using a concrete model, have children do the following Penny Grab activity.
1. Place a pile of pennies or other counters on a table between two children.
2. Each child grabs a handful of pennies, counts them, and records the amount.
3. Partners compare their amounts by lining up the pennies side-by-side and finding the difference.
4. Partners work together to record number models that describe the lined-up pennies. For example, 9 - 6 = 3.
Encourage such remarks as, “I have 3 more than you. You have 3 less than I do.”
The difference between 9 and 6 is 3.
ENRICHMENT INDEPENDENTACTIVITY
� Comparing Number Stories 5–15 Min
(Math Masters, p. 161)
To further explore comparison number stories, have children complete Math Masters, page 161. Children compare number stories by writing number models and answering related questions.
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