Sketching Arrays & Partial Products 33877 - Amazon S3 · sketching arrays & partial products...

Quantile® Resource Overview

Resource Title: Sketching Arrays & Partial Products

Quantile Skills and Concepts:

• Multiply a multi-‐digit whole number by a 1-‐digit whole number or a 2-‐digit multiple of 10. (QSC165)

• Estimate and compute products of whole numbers with multi-‐digit factors. (QSC170)

Quantile Measure:

530Q

Excerpted from:

The Math Learning Center PO Box 12929, Salem, Oregon 97309-‐0929 www.mathlearningcenter.org ©Math Learning Center

For access to other free resources, visit www.Quantiles.com. The Quantile® Framework for Mathematics, developed by educational measurement and research organization MetaMetrics®, comprises more than 500 Quantile Skills and Concepts taught from kindergarten through high school. The Quantile Framework depicts the developmental nature of mathematics and the connections between mathematics content. By matching a student's Quantile measure with the Quantile measure of a mathematical skill or concept, you can determine if the student is ready to learn that skill, needs reinforcement in supporting concepts first, or whether enrichment would be appropriate. For more information and to use free Quantile utilities, visit www.Quantiles.com.

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set a5 number and Operations: multi-digit multiplication

Bridges in Mathematics Grade 4 Supplement • a5.55© The Math Learning Center

set a5 H Activity 8

activity

sketching arrays & partial products

OverviewThe teacher introduces a technique for drawing quick

sketches of 2-digit by 2-digit multiplication combinations.

Students then practice the sketching technique and use it

to solve a variety of multiplication problems.

skills & ConceptsH represent multiplication of two-digit by two-digit

numbers

H multiply two-digit by two-digit numbers

H estimate products to approximate solutions and

determine reasonableness of answers

You’ll needH The Ladybugs’ Park (page A5.58, run one copy on a

transparency)

H Multiplication Sketches (pages A5.59 and A5.60, run a

class set)

H overhead pens

H a piece of paper to mask portions of the overhead

Instructions for sketching arrays & partial products 1. Place the top section of The Ladybugs’ Park on display at the overhead. Read the problem with the class. Ask students to estimate the area of the sandbox, and call on volunteers to share their thinking with the class.

Set A5 Number and Operations: Multi-Digit Multiplication Blackline Run 1 copy on a transparency.

The Ladybugs’ Park

1 The ladybugs over in Leafi ngton are building a park for their children. They are planning to make a sandbox that is 12 centimeters wide and 18 centimeters long. How many square centimeters will their sandbox be?

2 There is patch of dirt near the sandbox that measures 24 by 29 centimeters. The ladybugs want to divide it into different sections as shown below. Use a mul-tiplication equation to label each section. Then fi nd the total area of the 24 by 29 cm patch.

Play Area Picnic Tables

29 cm

24 cm

Flower Bed Fountain

Students I think about 210 square centimeters because 10 × 18 is 180, and then 2 × 18 is 36. I said 200 because 12 × 18 is kind of like 10 × 20, and that’s 200.

2. As students watch, sketch a frame for 12 × 18 at the overhead. Then fill in the array as shown at the top of the next page. Let students know that you are drawing lines based on the place values in the di-mensions (between the 10 and the 8 in 18, and the 10 and the 2 in 12).

3. After you have drawn in the lines, ask the students to help you fill in the area of each part of the ar-ray. Prompt their thinking, if necessary, by labeling the tens and ones on the frame.


© The Math Learning Centera5.56 • Bridges in Mathematics Grade 4 Supplement

12 cm

18 cm

12 cm

18 cm

10

2

10 8

10 x 10 = 100

4. After you’ve labeled all 4 parts of the array, remind students that each part is called a partial product, and that the sum of the partial products is the total product of 12 × 18. Then ask students to find the sum of the partial products mentally. Record their thinking as an equation beside the array. Also record a multiplication equation to show the dimensions and total area together.

12 cm

18 cm

10

2

10 8

10 x 10 = 1001008020

+ 1 6

10 x 8 = 80

2 x 10 = 20 2 x 8 = 16 2 1 6 sq cm

1 8x 1 2

2 1 6 sq cm

5. Repeat Steps 1–4 with the second problem on the overhead.






29 cm

24 cm

Flower Bed Fountain






29 cm

24 cm

Flower Bed Fountain

20

20 x 20 = 400 20 x 9 = 180

4 x 20 = 80

4001 80

80+ 3 6

4 x 9 = 36

20

4

9

6 9 6 sq cm

4001 80

29x 246 9 6 sq cm

6. Now give students each a copy of the Multiplication Sketches worksheets. Ask them to complete the first problem on their own or in pairs. Circulate as they work, and then reconvene the class to discuss their thinking when most are finished. Walk through the problems step by step as a whole group, start-ing with a sketch of the array on the whiteboard that replicates the picture on the first worksheet and finishing with an addition and a multiplication equation to express the total area.

activity 8 Sketching Arrays & Partial Products (cont.)



16 cm

28 cm

10

6

20 8

10 x 20 = 200 20080

1 20+ 4 8

10 x 8 = 80

6 x 20 = 120 6 x 8 = 48 448 sq cm

28x 1 6

448 sq cm

7. When students understand what to do, have them complete the rest of the first sheet and all of the second independently. Provide assistance as needed. Encourage students to share and compare their an-swers as they finish the assignment.

NAME DATE

Set A5 Number and Operations: Multi-Digit Multiplication Blackline Run a class set.

Double-digit Multiplication Sketches page 1 of 2

1a Mrs. Hill’s pre-school classroom is 16 feet wide and 28 feet long. She is plan-ning to divide it into 4 sections. Here is her plan. Use a multiplication equation to label the area of each section. (in square feet)

Rug Tables

28´

16´

Art Area Library Corner

b What is the total area of the 16-by-28-foot classroom? Show your work.

2 Write the answers. 20 30 50 40 10 60 30 × 30 × 40 × 30 × 20 × 90 × 30 × 30 _____ _____ _____ _____ _____ _____ _____

iNDEPENDENt WORKShEEt

Use Set A5 Independent Worksheet 6 to provide students with more practice multiplying multiples of 10 by multiples of 10.

NAME DATE

Set A5 Number and Operations: Multi-Digit Multiplication Blackline Run a class set.

Double-digit Multiplication Sketches page 2 of 2

3 Sketch an array for each of the frames below. Label each part with a multipli-cation equation to show its area. Then fi nd the total product of the array.

a26

13

b15

14

c23

17


activity 8 Sketching Arrays & Partial Products (cont.)


set a5 number and Operations: multi-digit multiplication Blackline Run 1 copy on a transparency.

the ladybugs’ park

1 The ladybugs over in Leafington are building a park for their children. They are planning to make a sandbox that is 12 centimeters wide and 18 centimeters long. How many square centimeters will their sandbox be?

2 There is patch of dirt near the sandbox that measures 24 by 29 centimeters. The ladybugs want to divide it into different sections as shown below. Use a mul-tiplication equation to label each section. Then find the total area of the 24 by 29 cm patch.


29 cm

24 cm

Flower Bed Fountain


name date

set a5 number and Operations: multi-digit multiplication Blackline Run a class set.

double-digit multiplication sketches page 1 of 2

1a Mrs. Hill’s pre-school classroom is 16 feet wide and 28 feet long. She is plan-ning to divide it into 4 sections. Here is her plan. Use a multiplication equation to label the area of each section. (in square feet)

Rug Tables

28´

16´

Art Area Library Corner

b What is the total area of the 16-by-28-foot classroom? Show your work.



name date

set a5 number and Operations: multi-digit multiplication Blackline Run a class set.

double-digit multiplication sketches page 2 of 2

3 Sketch an array for each of the frames below. Label each part with a multipli-cation equation to show its area. Then find the total area of the array.

a

26

13

b15

14

c23

17


total area = _______

total area = _______ total area = _______

10 8

10

2

12 cm

18 cm

10 10 = 100

2 10 = 20

10 8 = 80

2 8 = 16

100802016

216 sq cm

1812

216 sq cm

4001808036

696 sq cm

2924

696 sq cm

20 20 = 400 20 9 = 180

4 20 = 80 4 9 = 36

10 20 = 200 10 8 = 80

6 20 = 120 6 8 = 48

20012080+48448 sq ft

2816448 sq ft

600 1200 1500 800 900 1800 900

10 20 = 200 10 6

3 20 = 60 3 6 = 18

= 60

2006060

+18338 sq units

2613

338 sq units

338 sq units

10 10 = 100 10 5

4 10 = 40 4 5

= 50

= 20

10 20 = 200

7 20 = 140

10

3 = 30

7

3 = 21

391sq units

180 320 350 280 240 300 640

210 sq units

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