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Interactive Teacher’s
Lesson Guide
CurriculumFocal Points
Family Letters
EM Facts Workshop Game™
Algorithms Practice
eToolkitePresentations AssessmentManagement
Common Core State Standards
412 Unit 6 Whole-Number Operations and Number Stories
Advance PreparationFor the optional Extra Practice activity in Part 3, obtain the book Each Orange Had 8 Slices:
A Counting Book by Paul Giganti, Jr. (Greenwillow Books, 1992).
Teacher’s Reference Manual, Grades 1–3 pp. 90, 91
Key Concepts and Skills• Count the total number of objects in
several groups.
[Number and Numeration Goal 1]
• Make arrays to represent equal groups.
[Operations and Computation Goal 4]
• Use various strategies to solve
equal-groups number stories.
[Operations and Computation Goal 4]
Key ActivitiesChildren are introduced to diagrams to
identify the known and unknown quantities
in multi plication problems and to complete
number models to summarize the solutions.
Children also solve number stories about
equal groups of things.
Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Operations and Computation Goal 4]
Key Vocabularyequal groups � multiplication � times �
multiplied by
MaterialsMath Journal 1, p. 148
My Reference Book, pp. 112 and 113
Home Link 6�6
Math Masters, p. 415
per group: 40 pennies or other counters �
6 boxes or bags to hold pennies or other
counters (for demonstration) � pennies or
other counters (for demonstration)
Practicing with +/- Fact Triangles+/- Fact Triangles in an envelope
Children use Fact Triangles to practice
addition and subtraction facts.
Math Boxes 6�7Math Journal 1, p. 149
Children practice and maintain skills
through Math Box problems.
Home Link 6�7Math Masters, p. 179
Children practice and maintain skills
through Home Link activities.
READINESS
Finding Totals for Equal GroupsMath Masters, p. 180
calculator
Children use their calculators and repeated
addition to solve equal-groups problems.
ENRICHMENTSolving Equal-Groups RiddlesMath Masters, p. 181
Children create and solve equal-groups
number riddles.
EXTRA PRACTICE
Equal Groups in LiteratureEach Orange Had 8 Slices: A Counting Book
Children identify and solve multiplication
problems found in literature.
ELL SUPPORT
Building a Math Word BankDifferentiation Handbook, p. 142
Children add the term multiplication to their
Math Word Banks.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
Multiplesof Equal Groups
Objective To introduce multiplication as a way to find the total
number of things in several equal groups.
�������
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Lesson 6�7 413
�
5 + 5 + 5 = 15
105 15
1 pack
1 pack 15 sticks
1 pack}
////\
////\
////\
////\
////\ ////\
Some solution strategies for the Math Message
problem
Getting Started
Home Link 6�6 Follow-Up Children draw the different arrays they made with 24 Xs. Be sure to include the following arrays: 1 row of 24 Xs and 24 rows of 1 X each. Show children any other possible arrays that they do not suggest.
Mental Math and ReflexesHave children share strategies for solving comparison number stories like the following:
Vivianna is 40 inches tall. Jennifer is 30 inches tall. How much taller is Vivianna than Jennifer? 10 inches taller
Cecilia’s pencil was 19 centimeters when it was new. Now it is 9 centimeters shorter. How long is Cecilia’s pencil now? 10 centimeters long
Josh caught a fish that was 15 inches long. Jackie caught a fish that was 7 inches longer. How long was Jackie’s fish? 22 inches
Math MessageJane bought 3 packs of gum. There are 5 sticks of gum per pack. How many sticks of gum did she buy? Show how you found your answer on an Exit Slip ( Math Masters, page 415).
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
Ongoing Assessment: Math Message �
Recognizing Student Achievement
Use the Math Message to assess children’s understanding of combining equal
groups to find the total. Children are making adequate progress if they can find
the answer by counting by 1s, 5s, drawing a picture, creating tally marks, or
adding the equal groups. Some children may be able to write a multiplication
number model for the problem.
[Operations and Computation Goal 4]
Ask children to share their solution strategies. Expect a variety of strategies: count by 1s; count by 5s; add 5s; double 5, and then add 5. Some children might draw pictures or use tallies. (See margin.)
Use the Math Message problem to lead into a discussion about equal groups. Write equal groups on the board. Ask children to name things that come in equal groups and write their responses on the board. To support English language learners, draw pictures of any unfamiliar contexts. In the Math Message problem, the packs of gum are equal groups, because each pack has five sticks of gum in it. Six-packs of soft drinks are another familiar example of equal groups, because each six-pack has six cans or bottles in it. Ask children to name things that do not come in equal groups. Sample answers: Families, classroom sizes
ELL
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414 Unit 6 Whole-Number Operations and Number Stories
Tell children that they can find the total number of things in several equal groups by multiplication. Emphasize that in a multiplication situation, each group must have the same number of things.
Show children some possible number models for the number story: 5 + 5 + 5 = 15 or 3 × 5 = 15. Mention that 3 × 5 is read “3 times 5” or “3 multiplied by 5.” To support English language learners, review the meaning of times in this context.
� Solving Number Stories WHOLE-CLASS ACTIVITY
about Equal Groups
Algebraic Thinking Divide the class into groups of 4 or 5. Display several boxes of an item, such as pennies, paper clips, dominoes, or crayons. Each box should contain the same number of the item selected.
Example: Display five boxes and put four pennies in each one. Tell the class that there are four pennies per box. Ask children to find the total number of pennies in all the boxes by using counters to act out a solution.
Suggested questions:
● How many groups of pennies are there? 5, because there are 5 boxes
● How many pennies are in each group? 4 Are they equal groups? Yes, because there is an equal number of pennies in each box.
● How many pennies are there in all? 20
● What number model can we write for this problem?5 × 4 = 20 or 4 + 4 + 4 + 4 + 4 = 20
Draw a diagram on the board that identifies the known and unknown quantities. Point out that the numbers in the diagram tell the quantities we know and that the question mark indicates the quantity we are trying to find. Once children have found the answer, erase the question mark, write in the answer 20, and circle it. (See below.)
boxes pennies per box pennies in all
5 4 20
5 × 4 = 20
4 + 4 + 4 + 4 + 4 = 20
Make up other stories by changing the number of boxes and the number of items per box. Emphasize the language of equal groups: for example, three boxes with seven marbles per box and three boxes with seven crayons in each box.
PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBLBBLBLBLLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELELELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB ELEELELEMMMMMMMMMOOOOOOOOOBBBLBLBLBBBLBBLOOROROROORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINNNNVINVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOLOOLOLOLOO VVINVINLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLLOOO VVVLLLLLLLLLLVVVVVVVVVVOSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOOSOOSOSOSOSOSOSOSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVLLLLLLLLVVVVVVVVVLLLVVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING
ELL
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Adjusting the Activity
Lesson 6�7 415
Multiplication StoriesLESSON
6 �7
Date Time
Solve each problem. Draw pictures or use counters to help.
Example: How many cans are in three 6-packs of juice?
/// /// /// /// /// /// 6 12 18
Answer: 18 cans
1. Mr. Yung has 4 boxes of 2. Sandi has 3 bags of marbles.markers. There are 6 markers Each bag has 7 marbles in it.in each box. How many How many marbles does shemarkers does he have in all? have in all?
Answer: markers Answer: marbles
3. Mrs. Jayne brought 4. After the picnic, 5 boys each5 packages of buns to picked up 4 soft-drink cans tothe picnic. Each package recycle. How many cans did had 6 buns in it. How many the boys pick up all together? buns did she bring in all?
Answer: buns Answer: cans
24
30
21
20
EM3MJ1_G2_U06_131_158.indd 148 1/29/11 9:44 AM
Math Journal 1, p. 148
Student Page
Mia has 4 packs of gum.There are 5 sticks of gum in each pack.How many sticks of gum are there in all?
packs sticks per pack sticks in all
4 5 ?
Number of groups
You know thenumber of groups.
You know thenumber of objects
in each group.
You don’t knowthe total number
of objects.
Total number of objects
Number of objects in each group
Number model: 4 5 ?
You can use a diagram to help you solve a number story about groups with equalnumbers of objects.
Number Stories
My Reference Book, p. 112
Student PageChildren should continue using counters, pictures, doodles, or anything else that might help them find the total number of items. As they share solution strategies, write number models on the board and read the models aloud. For example:
� 5 + 5 + 5 = 15 5 plus 5 plus 5 equals 15.
� 3 × 7 = 21 3 times 7 is 21.
� 4 × 6 = 24 6 multiplied by 4 equals 24.
Continue to fill in a diagram for each of the problems on the board. Write in the known quantities, and write a question mark for the unknown quantity. Ask children to help you complete the diagrams as you discuss problems, but do not expect children to come up with diagrams on their own. Repeated exposure to such diagrams will help children understand the meanings of multiplication and division.
Next, make up several number stories that do not require boxes of items as props. Fill in diagrams as before. As children share solutions, write number models on the board. Suggestions:
6 children have wet shoes, 2 shoes per child. How many wet shoes? 12
3 children took 4 crackers each. How many crackers? 12
4 packs of juice, 6 cans per pack. How many cans? 24
2 weeks, 7 days per week. How many days? 14
Pose problems using larger numbers. For example:
• 3 hours, 50 miles per hour. How many miles? 150
• 5 toys, 99 cents per toy. Total cost? $4.95
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
� Solving Number Stories PARTNER ACTIVITY
about Equal Groups(Math Journal 1, p. 148; My Reference Book,
pp. 112 and 113)
Algebraic Thinking You may wish to read about number stories with equal groups in My Reference Book, pages 112 and 113 with your class. Partners act out and solve the multiplication stories on the journal page. Ask them to show how they solved the problems. Children might draw pictures or use counters.
PROBLEMBBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMEEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOBBBLBLBBLBLBLLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPROPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEELELELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB EEEMMMMMMMMOOOOOOOOOBBBBBBBBBOOORORORORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGGLLLLLLLLLLLLVINVVINVINVINVINNNNVINVINVINVINVINVINGGGGGGGGGGGOLOOOLOLOLOLOLOLOO VINVINVVINLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVIVINVINV NGGGGGGGGGGOLOOLOLOLOLOLOLOOO VVVVVVVLLLLLLLLLLVVVVVVVVVSOSOSOOSOSOSOSOOSOOSOSOSOSOSOOOOOSOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLVVVVVVVVVLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
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416 Unit 6 Whole-Number Operations and Number Stories
Name Date Time
In today’s lesson, your child learned that multiplication is an operation used to find the total number of things in several equal groups. As you help your child solve the following problems, emphasize that each group has the same number of things. Your child can use objects, draw pictures, count, or use any other helpful devices to find the answers.
Please return this Home Link to school tomorrow.
1 pica to top rule1 pica to left rule
style sheet: No Style
char style: G1_MM Prob Num bol
HOME LINK
6�7 How Many?
Example: How many apples in 4 packages?
There are 20 apples in 4 packages.
1.
How many sides on each triangle? sides
How many sides in all? sides
2.
How many wheels on each bike? wheels
How many wheels in all? wheels
3. How many fingers for each person?
fingers
How many fingers in all?
fingers
82
183
80
10
5 � 5 � 5 � 5 � 20
////\ ////\ ////\\\ ////\\\
Family Note
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Math Masters, p. 179
Home Link Master
Math BoxesLESSON
6 �7
Date Time
1. Write the number.
2. Make ballpark estimates. Write a number model foreach estimate.
32 + 59
+ = 51 + 27
+ =
Unit
cm
4.
How many? Cross out 23 cubes.
How many are left? Write a number model.
- =
5. Lauren’s birthday is on the tenth day in the shortest month of the year. In what month is her birthday?
6. Double.
2 4 10 50
3. Measure the line segment.
Draw a line segment 3 cm shorter.
Unit
10 11
31
85
92–94
32530
50
60
30
90
80
51
28
282351
4820100
9
Sample estimates.
February
EM3MJ1_G2_U06_131_158.indd 149 1/29/11 10:57 AM
Math Journal 1, p. 149
Student Page
2 Ongoing Learning & Practice
� Practicing with PARTNER ACTIVITY
+/- Fact TrianglesHave children work with a partner using the Fact Triangles as flash cards. Remind children that when their partner misses a fact, they should flash the other fact problems on the triangle and then return to the fact that was missed.
� Math Boxes 6�7 INDEPENDENTACTIVITY
(Math Journal 1, p. 149)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-9. The skill in Problem 6 previews Unit 7 content.
Writing/Reasoning Have children draw, write, or verbalize their answers to the following: In Problem 5, if Lauren was born the same year as you, is she older or younger? What strategy did you use to solve the problem?
Sample answer: She is older than me; I was born in June, so she would turn 8 years old first. She is younger than me, I was born in January, so I would turn 8 years old first.
� Home Link 6�7 INDEPENDENTACTIVITY
(Math Masters, p. 179)
Home Connection Children can use objects, draw pictures, count, or use any other helpful device to solve problems about equal groups.
3 Differentiation Options
READINESS
INDEPENDENTACTIVITY
� Finding Totals for Equal Groups 5–15 Min
(Math Masters, p. 180)
To provide experience with solving equal-groups problems, have children use their calculators and repeated addition. Some children may want to program the calculator to skip count, while others may want to enter + repeatedly. When they have finished solving the problems, have them compare their answers. They should rework problems on which they don’t agree. Have volunteers share their strategies for solving the problems. Consider having children record addition number sentences to show how they solved problems.
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You may use your calculator to help you solve the problems.
1. How many people are in my group?
How many hands do the people in my group have all together?
How many fingers do the people in my group have all together?
2. How many tables are in the classroom?
How many legs do the tables have?
3. One flower has 5 petals.
How many petals do 6 flowers have?
4. Make up your own problem like the ones above. Draw a picture to help someone solve your problem.
LESSON
6�7
Name Date Time
Finding Totals for Equal Groups
Answers vary.
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Math Masters, p. 180
Teaching Master
What Number Am I?
1. If you put me into 7 equal groups with 3 in each group and 5 are left over, what number am I?
Draw a picture of what you did. Sample answer:
2. I am a number between 20 and 30. When you put me into 6 equal groups, there is an even number in each group and 1 is left over.
What number am I?
Draw a picture of what you did. Sample answer:
3. Try writing your own equal-groups riddle.
25
26
Name Date Time
LESSON
6�7 Equal-Groups Riddles
Answers vary.
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Math Masters, p. 181
Teaching Master
Lesson 6�7 417
ENRICHMENT SMALL-GROUP ACTIVITY
▶ Solving Equal-Groups Riddles 15–30 Min
(Math Masters, p. 181)
To further explore the concept of equal groups, have children use Math Masters, page 181 to create and solve equal-groups riddles.
EXTRA PRACTICE SMALL-GROUP ACTIVITY
▶ Equal Groups in Literature 15–30 Min
Read the following book to groups of children, or have children read the book themselves.
Each Orange Had 8 Slices: A Counting Book by Paul Giganti, Jr. (Greenwillow Books, 1992) Summary: Multiplication concepts are explored in the full-color book. In the first presentation, 3 red flowers are seen; each flower has 6 petals, and each petal has 2 black bugs. Questions are posed about the number of flowers, the number of petals, and the number of bugs. Have children answer the questions posed in the book.
ELL SUPPORT SMALL-GROUP ACTIVITY
▶ Building a Math Word Bank 5–15 Min
(Differentiation Handbook, p. 142)
To provide language support for multiplication, have children use the Word Bank template found on Differentiation Handbook, page 142. Ask children to write the term multiplication, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.
Planning Ahead
Have children copy their Beat the Calculator results from Math Journal 1, page 24 to Math Journal 2, page 311. Children will continue to record the facts for which they can beat the calculator. The Fact Power Table on journal page 311 will become a cumulative record of children’s progress toward addition fact power during Beat the Calculator game situations.
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