www.everydaymathonline.com Interactive Teacher’s Lesson Guide Curriculum Focal Points Family Letters EM Facts Workshop Game™ Algorithms Practice eToolkit ePresentations Assessment Management Common Core State Standards 418 Unit 6 Whole-Number Operations and Number Stories Advance Preparation In Part 1, choose one of the following to display a multiplication diagram and its corresponding array: • Make an overhead transparency of Math Masters, page 438. • Draw and erase multiplication diagrams, arrays, and number models on the board as needed. For an additional mathematics and literacy connection, obtain copies of Sea Squares by Joy N. Hulme (Hyperion Books for Children, 1999) and Amanda Bean’s Amazing Dream by Cindy Neuschwander (Scholastic Inc., 1998). Teacher’s Reference Manual, Grades 1–3 pp. 90–92 Key Concepts and Skills • Solve multiplication number stories using rectangular arrays. [Operations and Computation Goal 4] • Create multiplication number stories using rectangular arrays. [Operations and Computation Goal 4] • Write a number model that represents a rectangular array. [Patterns, Functions, and Algebra Goal 2] Key Activities Children identify and describe familiar arrays, create and solve number stories about arrays using multiplication diagrams and array models, and complete number models to summarize solutions. Ongoing Assessment: Recognizing Student Achievement Use journal page 151. [Operations and Computation Goal 4] Key Vocabulary multiplication diagram x-by-y array Materials Math Journal 1, pp. 150 and 151 Home Link 6 7 Math Masters, p. 182 (optional); pp. 183 and 438 transparency of Math Masters, p. 438 (optional) per partnership: 50 pennies or other counters (optional) calculator Playing the Fact Extension Game My Reference Book, pp. 134 and 135 per partnership: 4 each of number cards 0–9 (from the Everything Math Deck, if available), 2 sheets of paper, 1 die, calculator Children practice fact extensions. Math Boxes 6 8 Math Journal 1, p. 152 Children practice and maintain skills through Math Box problems. Home Link 6 8 Math Masters, p. 183 Children practice and maintain skills through Home Link activities. READINESS Playing Simon Says 24 counters Children practice making equal rows using a concrete model. ENRICHMENT Creating Array Number Stories Math Masters, p. 419 Children write number stories, draw an array for the number story, and write a number model to represent the story. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 142 Children add the term array to their Math Word Banks. Teaching the Lesson Ongoing Learning & Practice 1 3 2 4 Differentiation Options Array Number Stories Objectives To introduce everyday examples of rectangular arrays; and to provide experiences with solving multiplication problems using multiplication diagrams and array models. a
Transcript
www.everydaymathonline.com
Interactive Teacher’s
Lesson Guide
CurriculumFocal Points
Family Letters
EM Facts Workshop Game™
Algorithms Practice
eToolkitePresentations AssessmentManagement
Common Core State Standards
418 Unit 6 Whole-Number Operations and Number Stories
Advance PreparationIn Part 1, choose one of the following to display a multiplication diagram and its corresponding array:
• Make an overhead transparency of Math Masters, page 438.
• Draw and erase multiplication diagrams, arrays, and number models on the board as needed.
For an additional mathematics and literacy connection, obtain copies of Sea Squares by Joy N. Hulme (Hyperion
Books for Children, 1999) and Amanda Bean’s Amazing Dream by Cindy Neuschwander (Scholastic Inc., 1998).
Teacher’s Reference Manual, Grades 1–3 pp. 90–92
Key Concepts and Skills• Solve multiplication number stories using
rectangular arrays.
[Operations and Computation Goal 4]
• Create multiplication number stories using
rectangular arrays.
[Operations and Computation Goal 4]
• Write a number model that represents a
rectangular array.
[Patterns, Functions, and Algebra Goal 2]
Key ActivitiesChildren identify and describe familiar arrays,
create and solve number stories about arrays
using multiplication diagrams and array
models, and complete number models to
summarize solutions.
Ongoing Assessment: Recognizing Student Achievement Use journal page 151. [Operations and Computation Goal 4]
Have children share how they solved the problem on their calculator.
For example:
� I entered 6 + 6 on my calculator. (all calculators)
� I entered 6 X 2
=
. (all calculators)
� I entered 2 + ,
=
,
=
,
=
,
=
,
=
,
=
. (on the TI-108)
� I entered 2 , , , , . (on the Casio SL-450)
If children do not mention the 6 X 2 option, be sure to point it
out and have children solve the Math Message by entering
6 X 2
=
. Explain that this key is the standard multiplication key and that they will have an opportunity to use this key in later lessons.
Next, ask someone to draw the egg carton on the board. Remind children that an array is a rectangular arrangement of objects in rows and columns and point out that the eggs form an array. There are 2 rows of eggs with 6 eggs in each row, so there are 12 eggs in all.
Display a multiplication diagram. (See Advance Preparation.) Fill it in. Mark or draw a 2-by-6 array and write number models as shown in the margin.
Getting Started
Math MessageEgg carton: 2 rows of 6 eggs. Use your calculator to find how many eggs in all. 12 eggs
Home Link 6�7 Follow-Up Review answers. Ask children to write number models for each problem and to read them aloud. 6 × 3 = 18, 2 × 4 = 8, 8 × 10 = 80
Mental Math and Reflexes Pose number stories about multiples of equal groups.
Suggestions:
Yuko has 2 boxes of crayons. There are 8 crayons in each box. How many crayons in all? 16
Arlie can walk about 3 miles per hour. About how many miles can he walk in 4 hours? About 12 miles
Each apple costs 25 cents. Jenna bought 5. How much did she pay? $1.25
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420 Unit 6 Whole-Number Operations and Number Stories
150 f f
Array Number StoriesLESSON
6 � 8
Date Time
Array
Array
Array
Array
rows per row in all
Multiplication Diagram
Number model:
rows per row in all
Multiplication Diagram
rows per row in all
Multiplication Diagram
rows per row in all
Multiplication Diagram
Number model:
Number model:
Number model:
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Math Journal 1, p. 150
Student Page
Adjusting the Activity
py
gg
p
Family Note
Name Date Time
In this lesson, your child solved multiplication problems about arrays, which are rectangular arrangements of objects in rows and columns. Encourage your child to use counters, such as pennies or buttons, while working on the following exercises.
Distribute Home Link 6-8. At the bottom it includes pictures of six familiar arrays. For each array, ask children how many rows there are and how many items there are in each row. Encourage them to talk about x-by-y arrays. For example:
� Telephone: 4 rows of keys, 3 keys in each row; a 4-by-3 array
� Checkerboard: 8 rows of squares, 8 squares per row; an 8-by-8 array
2-by-6 arrays: 2 rows, 6 per row
Draw the 2-by-6 dot array on the board. Explain that there are different
ways to describe the array and write the following statements on the board.
2-by-6 Array
2 Rows and 6 Dots in each Row
2 Rows and 6 Dots per Row
To support English language learners, clarify that the word per can
replace the words in each.
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
� Creating and Solving Number WHOLE-CLASS ACTIVITY
Stories about Arrays(Math Journal 1, p. 150; Math Masters, p. 182)
Display a multiplication diagram.
You or the children make up number stories involving arrays of objects. (See the number-story suggestions on page 421.) For each story, children work alone or with a partner to do the following:
Solving Number Stories
1. Fill in the headings on the multiplication diagram on the journal page. For example, if the story is about rows of keys, fill in “keys” on the first line of the multiplication diagram.
2. Fill in the known numbers and write a question mark for the number to be found.
3. Make an array with counters to model the story.
4. Show the array next to the multiplication diagram by coloring the circles, drawing a ring around the circles, or marking the circles with Xs.
5. Write the answer on the diagram and circle it.
6. Write an addition or multiplication number model.
As children solve each problem, fill in the displayed diagram, mark or draw an array picture, and ask for the answer. Help children to summarize by writing a number model. A sample solution is shown below.
� Telephone: 4 rows of keys, 3 keys in each row. How many keys?
Number model: 3 + 3 + 3 + 3 = 12 or 4 × 3 = 12
Number-story suggestions:
� Carton of soup cans: 4 rows of cans, 6 cans per row. How many cans? 24
� Floor tiles: 5 rows of tiles, 9 tiles in each row. How many tiles? 45
� Tic-tac-toe: 3 rows of squares, 3 squares per row. How many squares? 9
� Math Boxes: 3 rows of problems, 2 problems in each row. How many problems? 6
� Calendar: 3 weeks, 7 days in each week. How many days? 21
Summary: Arrays are examples of equal groups of objects. The total number of objects in an array can be found by using repeated addition or multiplication.
Pose problems like these:
Theater seats: 15 rows of seats, 10 seats per row. How many seats? 150
Cases of soda: 10 cases of soda, 24 cans per case. How many cans? 240
Imagine a 20-by-30 array of dots. How many dots in all? Use your calculator to
solve. 600
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
ELL
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422 Unit 6 Whole-Number Operations and Number Stories
Math BoxesLESSON
6 �8
Date Time
1. Choose the best answer. Be careful!
6 tens
3 ones
8 hundreds
638 836
368 863
3. Use counters to solve. $14.00 is shared equally. Each child gets $5.00. How many children are sharing?
children How many dollars are left over?
dollars
6. What comes next?
2. Draw the line of symmetry.
4. This is a 5 -by- 4 array.
How many dots in all?
dots
5. Find the differences.
16°C and 28°C 70°F and 57°F 15°C and 43°C
60
88 89
2
4
121328
20
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Math Journal 1, p. 152
Student Page
Multiplication Number StoriesLESSON
6 � 8
Date Time
For each problem: � Use Xs to show the array.
� Answer the question.
� Write a number model.
1. The marching band has 3 rows with 2. Mel folded his paper into 2 5 players in each row. How rows of 4 boxes each. How many players are in the band? many boxes did he make?
There are players. He made boxes.Number model: Number model:
3. The sheet has 5 rows of stamps. 4. The orchard has 4 rows
There are 5 stamps in each row. of trees. Each row has 8 How many stamps are there? trees. How many trees are there?
There are stamps in all. There are trees.Number model: Number model:
� �
8
or 4 + 4 = 8or 5 + 5 + 5 = 15
5 + 5 + 5 + 5 + 5 = 25 or 8 + 8 + 8 + 8 = 32
32
15
25
5 × 3 = 15 2 × 4 = 8
5 × 5 = 25 or 4 × 8 = 32
EM3MJ1_G2_U06_131_158.indd 151 1/29/11 10:57 AM
Math Journal 1, p. 151
Student Page
� Solving Array Multiplication PARTNER ACTIVITY
Problems(Math Journal 1, p. 151)
Partners work together to draw arrays, solve problems, and write number models.
Use journal page 151, Problems 1 and 2 to assess children’s ability to show an
array. Children are making adequate progress if they can make the array and
count the total. Some children may be able to complete the number model.
[Operations and Computation Goal 4]
2 Ongoing Learning & Practice
� Playing the Fact Extension Game PARTNER ACTIVITY
(My Reference Book, pp. 134 and 135)
Children practice fact extensions through the Fact Extension Game first introduced on page 292 in Lesson 4-8. Directions for the game can be found on pages 134 and 135 in My Reference Book.
� Math Boxes 6�8 INDEPENDENTACTIVITY
(Math Journal 1, p. 152)
Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 6-6 and 6-10. The skill in Problem 6 previews Unit 7 content.
NOTE After children complete journal page 152, you may want to have them
create a shape using their Pattern-Block Template. Then have them use their
shape to create a pattern that involves flipping, sliding, or turning the shape.
� Home Link 6�8 INDEPENDENTACTIVITY
(Math Masters, p. 183)
Home Connection Children describe arrays and solve array problems.
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183
Name Date Time
In this lesson, your child solved multiplication problems about arrays, which are rectangulararrangements of objects in rows and columns. Encourage your child to use counters, such aspennies or buttons, while working on the following exercises.
Please return this Home Link to school tomorrow.
FamilyNote
HOME LINK
6�8 Arrays
Tell someone at home what you know about arrays.
1. Look at the arrayand fill in theblank.
4 rows of dots
6 dots in each row
dots in all.
2. Draw an array ofdots. Your arrayshould have
5 rows of dots
7 dots in each row
That’s dotsin all.
3. Draw an array of 12 dots.Sampleanswers: 1-by-12; 2-by-6; 3-by-4; 4-by-3; 6-by-2; 12-by-1
35
24
Telephone:a 4-by-3 array
Tic-tac-toe Grid:a 3-by-3 array
Muffins:a 3-by-2 array
Muffins:a 3-by-4 array
Checkerboard:an 8-by-8 array
Eggs:a 2-by-6 array
Math Masters, p. 183
Home Link Master
Unit
Name Date Time
A Number Story
Math Masters, p. 419
Teaching Aid Master
Lesson 6�8 423
3 Differentiation Options
READINESS SMALL-GROUP ACTIVITY
� Playing Simon Says 5–15 Min
To provide experience with making equal rows using a concrete model, have children play Simon Says where the directions are about modeling numbers in rows. Distribute 24 counters to each child. Give directions like the following:
● Simon says, “Put your counters in 4 equal rows.”
● How many counters are in each row? 6 counters
● Simon says, “Put your counters in rows with 3 in each row.”
● How many rows of counters are there? 8 rows
Be sure to discuss instances where children cannot make equal rows.
ENRICHMENT INDEPENDENTACTIVITY
� Creating Array Number Stories 15–30 Min
(Math Masters, p. 419)
To apply children’s understanding of array multiplication, have them write multiplication-array number stories on Math Masters, page 419. Children write the number stories in words, draw an array for the number story, and write a number model to represent the story.
Example:
Farmer Hannah planted 3 rows of corn. Each row had 9 corn stalks in it. How many corn stalks were there in all?
3 × 9 = 27 corn stalks
When children are finished writing their number stories, encourage them to trade with a partner and solve.
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 array, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.
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