Sketching Arrays & Partial Products 33877 - Amazon S3 · sketching arrays & partial products Overview The teacher introduces a technique for drawing quick ... Students then practice
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set a5 number and Operations: multi-digit multiplication
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.
set a5 number and Operations: multi-digit multiplication
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.
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
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
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.
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.
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.
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.
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.
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.