84 Number and Operations—Fractions Students need to understand how to add and subtract mixed numbers with like denominators before they can move on to more complex problems involving unlike denominators. Students will learn to replace mixed numbers with equivalent improper fractions and use their understanding of the operations of addition and subtraction to solve problems. Students will use concrete models to visualize the equivalent fractions and the given operation. Talk About It Discuss the Try It! activity. ■ Write 1 3 __ 4 + 2 1 __ 4 = on the board. Say: You can see the whole numbers you need to add, and the fractions you need to add. Circle 1 and 2 in one color and 3 __ 4 and 1 __ 4 in another color. Rewrite as 1 + 2 + 3 __ 4 + 1 __ 4 =, and add. ■ Say: You can add mixed numbers another way. You can change each number to an improper fraction. Have students refer to their BLMs and write the addition using improper fractions: 7 __ 4 + 9 __ 4 = 16 __ 4 = 4. ■ Say: Using improper fractions helps in subtracting mixed numbers. Suppose Denise and her brother drank 2 3 __ 4 cups of the punch. Change 2 3 __ 4 to an improper fraction. Ask: How much of the punch is left? Write 16 __ 4 – 11 __ 4 = 5 __ 4 on the board. Ask: How do you write 5 __ 4 as a mixed number? Extend the equation: 16 __ 4 – 11 __ 4 = 5 __ 4 = 1 1 __ 4 . Solve It With students, reread the problem. Have students draw and write the mixed numbers and have them write the addition with mixed numbers 1 3 __ 4 + 1 1 __ 4 = ? and with improper fractions 7 __ 4 + 9 __ 4 = ?. Then have them share their answers. More Ideas For other ways to teach about adding and subtracting mixed numbers— ■ Have students use Fraction Circles to solve the problem. ■ Have students use Cuisenaire ® Rods to solve the following problem: Ahmed has 4 1 __ 6 cups of potting soil. He used 2 5 __ 6 cups to plant a pepper plant. How much does he have left? (4 1 __ 6 – 2 5 __ 6 = 25 __ 6 – 17 __ 6 = 8 __ 6 = 1 2 __ 6 ) Formative Assessment Have students try the following problem. Jamal mixed 2 1 __ 3 cups flour with 1 1 __ 3 cups oats to make cookies. How many cups of the mixture does he have? A. 2 2 __ 3 cups B 3 1 __ 3 cups C 3 2 __ 3 cups D 4 cups 6
Transcript
84
Number and Operations—Fractions
Add and Subtract Mixed NumbersStudents need to understand how to add and subtract mixed numbers with like denominators before they can move on to more complex problems involving unlike denominators. Students will learn to replace mixed numbers with equivalent improper fractions and use their understanding of the operations of addition and subtraction to solve problems. Students will use concrete models to visualize the equivalent fractions and the given operation.
Talk About ItDiscuss the Try It! activity.
■ Write 1 3 __ 4 + 2 1 __ 4 = on the board. Say: You can see the whole numbers you need to add, and the fractions you need to add. Circle 1 and 2 in one color and 3 __ 4 and 1 __ 4 in another color. Rewrite as 1 + 2 + 3 __ 4 + 1 __ 4 =, and add.
■ Say: You can add mixed numbers another way. You can change each number to an improper fraction. Have students refer to their BLMs and write the addition using improper fractions: 7 __ 4 + 9 __ 4 = 16 __
4 = 4.
■ Say: Using improper fractions helps in subtracting mixed numbers. Suppose Denise and her brother drank 2 3 __ 4 cups of the punch. Change 2 3 __ 4 to an improper fraction. Ask: How much of the punch is left? Write 16 __
4 – 11 __
4
= 5 __ 4 on the board. Ask: How do you write 5 __ 4 as a mixed number? Extend the equation: 16 __
4 – 11 __
4 = 5 __ 4 = 1 1 __ 4 .
Solve ItWith students, reread the problem. Have students draw and write the mixed numbers and have them write the addition with mixed numbers 1 3 __ 4 + 1 1 __ 4 = ? and with improper fractions 7 __ 4 + 9 __ 4 = ?. Then have them share their answers.
More IdeasFor other ways to teach about adding and subtracting mixed numbers—
■ Have students use Fraction Circles to solve the problem.
■ Have students use Cuisenaire® Rods to solve the following problem: Ahmed has 4 1 __ 6 cups of potting soil. He used 2 5 __ 6 cups to plant a pepper plant. How much does he have left? (4 1 __ 6 – 2 5 __ 6 = 25 __ 6 – 17 __ 6 = 8 __ 6 = 1 2 __ 6 )
Formative AssessmentHave students try the following problem.
Jamal mixed 2 1 __ 3 cups flour with 1 1 __ 3 cups oats to make cookies. How many cups of the mixture does he have?
A. 2 2 __ 3 cups B . 3 1 __ 3 cups C . 3 2 __ 3 cups D . 4 cups
Objective
Common Core State Standards
■ 4.NF.3c
6
Number and Operations—Fractions
85
Materials• Fraction Tower® Equivalency Cubes• Fraction Towers (BLM 7; 2 per group)• colored pencils or crayons
Try It! 30 minutes | Groups of 4
Here is a problem about adding mixed numbers with like denominators.
Denise poured 1 3 __ 4 cups of cranberry juice into a pitcher. Then she added 2 1 __ 4 cups of apple juice to the pitcher to make a fruit punch. How many cups of
fruit punch are in the pitcher?
Introduce the problem. Then have students do the activity to solve the problem. Distribute materials to students.
1. Say: Use Fraction Towers to show the amount of cranberry juice. Have students use one whole tower and three 1 __ 4 cubes to model 1 3 __ 4 cup. Have them draw the model on the BLM. Ask students how the amount of apple juice should be modeled. Elicit that the model should be two whole towers plus one 1 __ 4 cube. Have them add that amount to the BLM and label each amount.
3. Have students put four 1 __ 4 towers together and place them next to one of the whole towers to show they are the same size. Ask: What do you notice about these towers? Say: Yes, they are the same. Four fourths are equal to 1. Have students write 4 __ 4 = 1 and 3 + 1 = 4.
2. Say: Now we need to add the items that are the same. Look at the towers. Ask: Do you see any towers that are the same? Elicit from students that the three whole towers are the same and the four 1 __ 4 towers are the same. Have students write 1 + 2 = 3 and 3 __ 4 + 1 __ 4 = 4 __ 4 .
4. Ask: How could you express each of the red towers in the model using yellow cubes? Elicit that each red tower can be replaced by a tower of 4 yellow cubes. Have them draw and color the all-yellow model on a second BLM and write the equation that expresses the model: 4 __ 4 + 3 __ 4 + 4 __ 4 + 4 __ 4 + 1 __ 4 = 16 __ 4 = 4.
Challenge! Two sisters were raising money for charity. Tia ran 5 1 __ 10 of a mile, while Jin walked 2 4 __ 10 mile. How many miles did they run/walk in all? How many less miles did Jin travel than Tia? Write the equations. Explain how to find the answers.
Answer Key
Download student pages at hand2mind.com/hosstudent.
Hands-On Standards, Common Core Editionwww.hand2mind.com
Challenge! Two sisters were raising money for charity. Tia ran 5 1 __ 10 of a mile, while Jin walked 2 4 __ 10 mile. How many miles did they run/walk in all? How many less miles did Jin travel than Tia? Write the equations. Explain how to find the answers.
