Welcome!2nd Quarter Curriculum Session

5th grade

Standard 5.NBT.7:

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

A Few Quick Points To build a conceptual understanding, students first

work with base ten blocks to model decimal multiplication.

They move from this concrete representation to more abstract representations, such as base ten shorthand, decimal grids, number lines and area models.

It is absolutely crucial that students reason about the products when working with decimals.

Students are not expected to multiply two decimal numbers that extend to the hundredths place value (or further)

A Few More Quick Points

The standard algorithm for multiplying decimals is not introduced. Although “students can summarize the results of their reasoning (about products)…to see the general pattern that the number of decimal places in the product is the sum of the number of decimal places in each factor.”

-DPI Unpacking Document

An example of such reasoning would be: “a tenth times a tenth is a hundredth (or one tenth of a tenth is a hundredth), so 3.2 x 7.1 will have an entry in the hundredths place.”

-DPI Unpacking Document

Another example of such reasoning is: “when they carry out the multiplication without the decimal point, they have multiplied each decimal factor by 10 or 100, so they will need to divide by those numbers in the end to determine the placement of the decimal.”

-DPI Unpacking Document

Decimal x Whole NumberReasoning

4 x 0.35What can we reason about the

product?

Now try with: 6 x .98 3 x .04

Decimal x Whole Number

Francine saw Kit Kat bars on sale for a great price and decided to buy one for each of her 4 closest friends. Each Kit Kat bar was on sale for $0.35 each. How much will Francine spend on her four friends?

First we’ll model with base ten pieces.

Decimal x Whole Number

Francine saw Kit Kat bars on sale for a great price and decided to buy one for each of her 4 closest friends. Each Kit Kat bar was on sale for $0.35 each. How much will Francine spend on her four friends?

0 1 2 3

Decimal x DecimalReasoning

What can we reason about the product?

2.7 x 3.2

Now try with: 0.2 x 0.9 5.8 x .04

Decimal x Decimal

Hunter’s favorite peaches are $2.70 a pound at the local farmers’ market. He bought 3.2 pounds of peaches. How much did he spend?

Decimal x Decimalones

ones

tenths

tenths

hundredths

2

3

0.7

0.2

+

+

6 2.1

0.4 0.14

0.7 x 0.2 = 0.140.7 x 3 = 2.12 x 0.2 = 0.42 x 3 = 6

62.10.4

+ 0.148.64

Decimal x Decimal

3.2 2.7x

Decimal x Decimal

Eventually students can make the transition to representing the previous problem in this way:

.73

.2

2

2 x 3 = 6

2 x .2 = 0.4

3 x .7 = 2.1

.2 x .7 = .14

6 + 2.1 + 0.4 + 0.14 = 8.64

+

+

Decimal Division

Coming later this month…

More details to follow

We hope you’ll be able to join us!

Thank you for your time!

Please email us if you have any further questions.

Remember to utilize the WCPSS YouTube channel to see short videos on the strategies we’ve shared with you today.