5th Grade Part 1-Multiplying Decimals SMART Board Teacher Notes

5.3 Number and Operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational numbers in order to solve problems with efficiency and accuracy. The student is expected to: (D) represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models.(S) (E) solve for products of decimals to hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers.(R)

Materials Part 1 - Multiply Decimals Smart Notebook File, Student Recording Document, 2 colors of markers or colored pencils for each student

Procedures As you work through the table and examples on the Smart Notebook file, consider the suggestions below:

Ask the students to predict if they think the product will be greater than 1 or less than 1 and to justify their thinking

Talk about real-life uses of decimal multiplication. Money is a great example. Ask students about the patterns they see and notice between the numbers being multiplied and the

productDay 1-Multiplying a whole number by a decimalSlide 2Before starting with the student recording sheet, ask students to look at the patterns that emerge when multiplying a decimal number by a whole number. As you pull the shade down, write the product for each. Let students record in their IMN. When you get to the decimals ask students what they think the answers will be based on the pattern.

What is the product of 2 and 800?This means 2 groups of 800, so 800 +800=1,600 or 2x800=1,600

What is the product of 2 and 80?This means 2 groups of 80, so 80+80=160 or 2x80=160

What is the product of 2 and 8?This means 2 groups of 8, so 8+8=16 or 2x8=16

What is the product of 2 and 0.8?This means 2 groups of 0.8, so 0.8+0.8=1.6 or 2x0.8=1.6

What is the product of 2 and 0.08?This means 2 groups of 0.08, so 0.08+0.08=0.16 or 2x0.08=0.16

What is the product of 2 and 0.008?This means 2 groups of 0.008, so 0.008+0.008=0.016 or 2x0.008=0.016

What patterns did you see and notice between the numbers being multiplied and the product?

Slides 4 –6 MATH_5 A MULTIPLY DECIMALS RECORDING SHEET 2014 RES Before shading the model, have your students estimate the product so they can check back to make sure their answer is reasonable.Instruct students to use two different colors to shade the models to differentiate between the equal groups when multiplying.Use the notes in the table on the following page to help facilitate your conversations. While the “explanation” column is lengthy, you can summarize these with your students.

Ask students about the patterns they see and notice between the numbers being multiplied and the products. Ask them to keep these patterns in mind as you work through the table.*Note: There are a variety of methods for the shading procedure.

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Expression Models ExplanationSummarize with students

Represent it in more than one way

A.

2 0.4

A 1x1 square has been divided into 10 columns and 10 rows. I shaded one group of 4 tenths in yellow. Then I shaded a second group of 4 tenths in green. Count all the shaded parts together.

2 0.4 = 0.8

80 out of 100 small squares are shaded.

80 out of 100 means 80100 or

810 , which is equal to 0.8

B.

4 0.18

A 1x1 square has been divided into 10 columns and 10 rows. I shaded one group of 18 hundredths in yellow. Then I shaded another group of 18 hundredths in green. I continued shading until I had 4 groups of 18 hundredths. Count the parts that are shaded.

4 0.18 = 0.7272 out of 100 small squares are shaded.

72 out of 100 means,72100

which is equal to 0.72

C.

2 x 1.89

Four 1x1 squares have been divided into 10 columns and 10 rows. Four squares are needed because both of the factors are greater than 1.

I shaded 1 whole, 8 tenths and 9 hundredths in yellow and then again in green. Count all the wholes then part of the last square.

2 1.89 = 3.78

3 wholes are shaded and 78 out of 100.

30078 out of 100 means,78100

which is equal to 0.78

Upon completing the table, ask students if they have noticed any patterns and have them summarize their thoughts on their recording document. (Students could recognize the “standard algorithm”, which indicates that when multiplying decimals; ignore the decimal points while you multiply the digits. Then, place the decimal in the product such that the total number of places after the decimal in the product is the same as the total number of places after the decimal in both factors. Also, students could notice the product is smaller than one of its factors.) It is important to let students discover this generalization.

Day 2-Multiplying a decimal by a decimalSlides 8 – 12

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Suggested IMN: Using the pizza recording sheet. Guide students using the SMART Board slide of the pizza to represent the pizza on their paper. Instruct students to fill in their name in the blank and circle the appropriate he/she in the problem. Now read the problem and shade in one color going vertically 0.5 or ½ of the pizza (Guide students to tell you 0.5 represents ½). Then, using another color shade 0.5 of the pizza going horizontally.(this should help students to connect to the model previously used, however in this problem they are taking part of a part, so their answer is represented by the double shaded piece). Students will shade the model below the pizza on their IMN sheet to match their pizza. Using the SB teachers can take the cloned grid and place it on top of the pizza to solidify the connection. Ask your students:How will we write this equation? (Since we are taking part of a part, we must multiply to find our answer.) Is our answer bigger or smaller than our factors? (Smaller which is different from our whole number multiplication.)

Use the notes in the table to help facilitate your conversations. While the “explanation” column is lengthy, you can summarize these with your students. Table for slides 9-12- MATH_5_ A_ MULTIPLY DECIMALS RECORDING SHEET 2014_RES

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Expression Models ExplanationSummarize with students Represent Another Way

E.

0.2 0.3

A 1x1 square has been divided into 10 columns and 10 rows. I shade 2 of the rows in one color to show two tenths and 3 of the columns in another color to show three tenths. Count the parts that are double shaded..

0.2 0.3 = 0.06

6 out of 100 small squares are double shaded.

6 out of 100 means

, which is equal to 0.06

F.

0.7 0.5

A 1x1 square has been divided into 10 columns and 10 rows. I shade 7 of the rows in one color to show seven tenths and 5 of the columns in another color to show five tenths. Count the parts that are double shaded.

0.7 0.5 = 0.3535 out of 100 small squares are double shaded.

35 out of 100 means

, which is equal to 0.35

G.

1.2 0.4

Two 1x1 squares have been divided into 10 columns and 10 rows. Two squares are needed because one of the factors is greater than 1.

I shade 4 of the rows in both squares in one color to show four tenths. I shade all of the columns in one square and 2 of the columns in the second square in another color to show one and two tenths. Count the parts that are double shaded.

1.2 0.4 = 0.48

48 out of 100 small squares are double shaded.

48 out of 100 means

which is equal to 0.48

H. Students choose 2 decimals less than one to the tenths place to multiply.

Ask students about the patterns they see and notice between the factors and the products and record their thinking on the record sheet* Note: Due to the commutative property you can shade columns then rows or rows then columns. Also, students could shade from the bottom of the grid to the top.

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Slide 13Compare and contrast the different ways that a whole number and a decimal can be multiplied.The examples use the distributive property, partial products, place value patterns, and algorithm. See below for possible explanations. Use MATH_5_A_MULTIPLYING DECIMALS 4 WAYS 2014_RES for student copies.

Slide 14MATH_5_A_MULT DECIMALS IMN PAGE 2014_RES-Student resource in iXploreThis is an example of the problem cards the students will receive for their IMN. Guide students through the process before they do their own card. Each student will receive a problem card. Students will glue the card into the left side of their IMN. Students will round the decimals to the nearest whole number. Using their rounded number, students will write and solve an estimation equation. Students will use their estimated product to determine where to place the decimal point. Students can then justify how they

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Introduce the distributive property: decomposed (break

down numbers into their subparts)

this makes the math easier and allow for mental math

students are not required to identify the property but utilize it help solve

similar to partial product method

partial product done in 4th grade

with whole number multiplication

students should reflect back to place value patterns and know that when you multiply a decimal by 10 and then 0.1 that the decimal point ends up in the same place

Ask the students to relate the other 3 back to the standard algorithm

decided where to place the decimal point. After the students have done their own card you can pull down the shade on the SB slide and discuss the pattern among the answers.Example Card:

Slides 15-18These slides can be used to reinforce the standard algorithm by clicking on box 2 (product estimation), box 3(whole number multiplication) and box 4(placement of decimal point). You can then prove your answer by revealing the model (box 1). Your students could work the problems in their IMN or dry erase. There is an additional slide to provide practice with multiplying with larger factors.

Slides 19-25Use the Guided Practice Problems (1-7) for students to work in partners with dry erase and model pages in page protectors (when needed). Problem #6 and #7 have a 4 digit factor which you may want to be sure to model for students. ***Please note that there are multiple representations of models for students to use. See the provided examples on the next pg. for possible models to use when multiplying involving decimals.

Slide 22Balloon Pop Guided Practice can be used as a warm up on Day 4 for students to practice predicting the number of decimal places in the product.

Additional Activity in iXplore:MATH_5_A_MULTIPLY DECIMALS SPINNER ACTIVITY 2014_RES.doc-Students will multiply decimals using the spinner recording sheet located in iXplore._

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12.4 x 1.8

~ Estimate ~

__ x __ = __

~ Place the decimal ~

2232

~ Justify ~

Since 12 x 2 = 24, I know the decimal would need to be between the 2 and

3, because my estimated product was the 2 digit whole number 24.

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