UNIT x 154 | UNIT 4 Instructional Routine: Mathematics p. Txxxii Fractions A • Identify purpose Direct students’ attention to the title and elicit the topic of the text. (adding and subtracting fractions) Remind students that texts have different purposes and elicit examples. (to compare, describe, explain, show how, define) Point out the subtitles and ask: What is the purpose of this text? Guide students to understand the purpose is to show how to use common denominators to add and subtract fractions and mixed numbers. • Build background knowledge Write ½ + ¾ on the board and ask students to identify the numerators and denominators. Point to the denominators and say: To add or subtract fractions you must have a common denominator and an equivalent fraction. Remind students that common means the same or alike and equivalent means same value. Work with students to determine the common denominator of ½ and 5/ 10 (10) and the equivalent fraction of ½ (5/ 10). Write _____ + 5/ 10 = ____, and ask a volunteer to complete the equation. (5/ 10 + 5/ 10 = 10/ 10 or 1) • Listen actively to build academic vocabulary Use the vocabulary routine to reinforce the meanings of add, subtract, multiply (X), common denominators, numerators, equivalent fractions, and mixed numbers. Play the audio and direct students to listen closely for these words as they follow along. Then replay the audio to build comprehension of the content. • Check comprehension Elicit examples of fractions, whole numbers, and mixed numbers. Have students demonstrate finding a common denominator for ¼ and 3/ 8 (8) then adding the fraction equivalent and fraction together. (2/ 8 + 3/ 8 = 5/ 8) Ask: Can you add and subtract mixed numbers? (yes) Ask volunteers to demonstrate the process and share examples. Essential question: How can you combine fractions with addition and subtraction? Use academic language Read aloud the Essential Question and elicit answers. Direct students to write examples on the board to support explanations. ANSWERS We use a common denominator. If there isn’t one, we find an equivalent fraction with a common denominator. EXPLORE AND LEARN DIFFERENTIATED INSTRUCTION Scaffold Gather students who need more support in a group to study terms and calculations. Have them take turns reading aloud common denominator and equivalent fractions in the text and leading the discussion to find definitions and examples, and explaining or performing calculations. Rephrase incorrect usage in a supportive way and help them understand mistakes in citing examples or performing calculations. Amplify Challenge students to determine common denominators and equivalent fractions for an additional set of fractions and mixed numbers. Then direct students to add or subtract the numbers and present their calculations to the class. Have students identify terms and describe calculations in complete sentences. Sample set: 3/ 8 + 2/ 16; 8/ 24 – 3/ 12; 1 ¾ + 5 ½; 150 7/ 16 – 25 ¼ UNIT 4 / CONNECT TO MATHEMATICS + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – – A Read the informational text. Adding and Subtracting Fractions Common Denominators To add or subtract fractions, the fractions must be the same size pieces. This means that they must have common denominators. Which fractions have common denominators? 1 2 3 4 6 8 1 4 8 4 2 3 If the fractions have the same denominator, then you can add the numerators. 3 4 + 1 4 = 4 4 If the fractions do not have the same denominator, find an equivalent fraction with a common denominator. 1 2 and 1 4 do not have the same denominator. Find an equivalent fraction for 1 2 with 4 as the denominator. 1 2 × 2 2 = 2 4 1 2 and 2 4 are equivalent fractions. Now the two fractions (2 4, 1 4) have a common denominator. You can add the fractions by adding the numerators. You can subtract the fractions by subtracting the numerators. 2 4 + 1 4 = 3 4 2 4 – 1 4 = 1 4 Mixed Numbers Some fractions are mixed numbers. 11 2 3 3 4 2 1 3 When you add or subtract with mixed numbers you need common denominators. You can change the mixed number into a fraction greater than 1. To do this, you can use a sketch. The picture at right represents 11 2, which is equivalent to 3 2. Here is another way to change a mixed number into a fraction greater than 1. Multiply the denominator by the whole part of the mixed number. Then, add the numerator. Write this total over the denominator. 1 2 1 2 1 2 11 2 = 3 2 1 1 2 = 3 2 × + Fractions How can you combine fractions with addition and subtraction? ? ESSENTIAL QUESTION 154 CONNECT TO Mathematics UNIT 4
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