Unit 5Multiplying Whole Numbers

by FractionsJanuary 10, 2013

Unit 5 Fraction Standards MCC4.NF.4 Apply and extend

previous understandings of multiplication to multiply a fraction by a whole number.

MCC4.NF.4a. Understand a fraction a/b as a multiple of 1/b.

MCC4.NF.4b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

MCC4.NF.4c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Visual Models

April wants to make a batch ofchocolate chip cookies and needs1/3 cup of chocolate chips.

How can the information in the problem be representedby a visual model?

If April makes two batchesof chocolate chip cookies,what fraction of a cup ofchocolate chips will be needed?

If April decides to make fourbatches of chocolate chip cookies,what amount of chocolate chipswill be needed?

How can this information berepresented by an additionequation?

By a multiplication equation?

How can a fraction model help to show 4 x 1/3 = 1 1/3?

1/3

1/3

1/3

1/3

1/3 1/3 1/3

Each day Courtney practices guitarfor 2/3 hour. In four days, howmany hours does she practice?

How many wholes would this equal?

How can this be indicated by an additionsentence?

Miguel fills 4 plastic cups withorange juice. Each plastic cupsholds 5/6 cups of orange juice. What is the total amount oforange juice?

Build one-whole using one colorof fraction pieces.

Write the multiplication equation for 5 times the fraction.

5 x 4/4 =20/4=5

=

If a bucket holds 1 5/6 gallons and5 buckets of water fill a tank,how much water does the tankhold?Write the multiplication equationand solve.

Counting Around the Class

0 1/4 2/4 3/4 4/4 5/4 6/4 7/4

1

8/4

2

Jake bought three kinds of pizza for aparty. Each pizza was the same size. People were not hungry, and at theend of the party there was ¾ of eachpizza left. How much pizza was left inall?

What equation could represent this problem?

1/4

1/4

1/4

1/4

1/4

1/4

1/4

1/4

1/4

3 x ¾ =

1/4

1/4

1/4

1/4

1/4

1/4

1/4

1/4

9/4

9/4 or 2 1/4

Eggs come in cartons of 12. Richard wasmaking cakes for a party and used 2cartons of eggs. How many eggs did heuse?Sabrina was making a cake for herself. She used ¼ of a carton of eggs. There are12 eggs in each carton. How many eggsdid she use?

Number of

Cartons

Number of Eggs in a Carton

Number of Eggs

Equation

1 2 12 24 2 x 12

2 1/4 12 3 ¼ x 12

A grocery store sells bags of 9apples. Anna used 2/3 of theapples in a bag in an apple pie. How many apples did she usein the pie?

Unit 6

Fractions and Decimals

MCC4.NF.5 Express a fraction withdenominator 10 as an equivalent fractionwith denominator 100, and use thistechnique to add two fractions withrespective denominators 10 and 100.

Find the tenths Decimal Square with 3 parts shaded.What is the fraction for the shaded amount of the square?Find the hundredths square with the same amount shaded? What fraction is shaded?Write an equation to show that these two squares have the same amount of shading.

To make purple paint, Josh mixes6/10 liter of red paint with 15/100liter of blue paint. How many litersof purple paint will he make?

Sally bought 5/10 pound of ham and25/100 pound of turkey. How manypounds of meat did Sally buy?

Tommy decided to mix some nutsthat he had shelled. He had 7/10pound of walnuts and 45/100 poundof cashews. How many pounds ofnuts did Tommy have?

MCC4.NF.6 Use decimal notationfor fractions with denominators10 or 100.

Decimal Notation

How do you write the decimalrepresented on this square? 0.8 or eight tenths

Decimal Notation

How do you write the decimalrepresented on this square? .35 or thirty-five hundredths

Relationship between decimals and fractions

Placing decimals on a number line

Place the decimal .5 on the number line.

Place the decimal .73 on the number line.

.5

.73

Placing decimals on a number line

Place the decimal 2.45 on the number line.Between what two numbers is the decimal 2.45?

2.45

MCC4.NF.7 Compare two decimals tohundredths by reasoning about their size.Recognize that comparisons are valid onlywhen the two decimals refer to the samewhole. Record the results of comparisonswith the symbols >, =, or <, and justify the

conclusions, e.g., by using a visual model.

Find the tenths square that has .6shaded. Describe the hundredthssquare with the same amountshaded and write it’s decimal.

Equality of Decimals

Find the hundredths square with45 parts shaded and write itsdecimal.

We can also think of this decimal as 4 tenths and 5 hundredths, since the first 4 columns have the same amount of shading as 4 columns on a tenths square.

Inequality of Decimals

Select two decimal squares, writethe decimal for each, and thenwrite an inequality statementusing the symbols >, <.

.50 >.35