UNIT X 34 | UNIT 1 Instructional Routine: Mathematics p. Txxxii Comparing and Ordering Numbers A • Build academic language Play the audio once, having students listen for general understanding. Play the audio again as students read along silently, paying special attention to the words in bold. • Use prior knowledge Ask students to share what they know about decimal numbers and fractions. Call on volunteers to write examples of both decimal numbers and fractions on the board. • Analyze numbers Explain to students how decimals and fractions are said aloud. Say: For decimals, we say the whole number first, and then the word point. Then we say the fractional numbers as individual numerals rather than whole numbers. Write 2.25 on the board. Say: First we say two then point, and then the fractional number is stated as two-five, not twenty-five. How do we say this decimal? (two point two-five) Then explain how to state fractions. Say: Fractions are expressed by saying the numerator as a cardinal number and the denominator as a plural ordinal number. Write 3/4 on the board and say: three-fourths. Then write the whole number 4 in front of the fraction. Say: To say a mixed fraction, you state the whole number, followed by the word and: “four and.” Ask: How do we say this fraction? (four and three-fourths) • Compare and order numbers Draw a large number line on the board as shown on page 34. Say: Number the number line with whole number parts (1, 2, 3). Number 1/4. What is 1/4 equivalent to as a decimal? (.25) Note that students can number the fractions on the top of the number line and the equivalent decimals on the bottom. Discuss which numbers are bigger and smaller. Elicit from students some rules that they can remember. Essential Question: How do people use decimals, fractions, and mixed numbers in everyday life? Read the Essential Question aloud and ask students to share their opinions. Write responses on the board. ANSWERS Sample answer: We use decimals, fractions, and mixed numbers when expressing measurements, like in cooking or when building things. EXPLORE AND LEARN DIFFERENTIATED INSTRUCTION Scaffold Measurements can be challenging for students to work with if they do not have concrete examples. Provide students with number lines, fraction resources, and decimal resources if possible. Amplify On graph paper, students draw five different fractions. Then they exchange papers with a partner who labels the fractions and provides the equivalent decimal numbers. ESSENTIAL QUESTION ? Comparing and Ordering Numbers A Read about comparing and ordering numbers. Does the state where you live get much rain, sleet, or snow? Do you live in a dry region of the United States? You might get a little or a great deal of precipitation each month, depending on where you live. Some precipitation amounts are recorded as decimals. Other amounts are recorded as fractions, and some are mixed numbers. We can record the amount of precipitation using whole numbers, decimals, fractions, or mixed numbers. Some values can be written in two different but equivalent ways. Some examples of fractions are 1 4,1 1 2, and 2 3 4. Some examples of decimals are 0.25, 1.5, and 2.75. When you look carefully, you can see that 1 4 and 0.25 are equal. The mixed number 11 2 and the decimal 1.5 are also equal. A number line is a helpful tool to represent a number’s value, put numbers in order, and compare numbers. How do people use decimals, fractions, and mixed numbers in everyday life? 1 4 0 1 2 3 1 21 3 42 0.25 0 1 2 3 1.5 2.75 CONNECT TO Mathematics 34 UNIT 1 UNIT 1 / CONNECT TO MATHEMATICS
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