Engage NY Math Module 3 Lesson 1: Making equivalent fractions with the number line, area model and with numbers.

Unit 3 Vocabulary Fraction = a numerical quantity that is not a whole number (e.g., 3 fifths or 3 5 ) Equivalent fraction = different fractions that name the same number (e.g., 3 5 = 6 10 ) Denominator = the number below the line in a common fraction; the divisor; the fractional unit (e.g., the 5 in 3 5 ) Numerator = the number above the line in a common fraction; the dividend; the count of fractional units (e.g., the 3 in 3 5 ) Like denominators = when the denominators in two or more fractions are the same (e.g., 3 5 and 1 5 ) Unlike denominators = when the denominators in two or more fractions are different (e.g., 3 8 and 1 7 ) Benchmark fractions = common fractions that you can compare other fractions against (e.g., 1 2, 1 3, 1 4, 2 3, and 3 4 ) Whole unit = e.g., any unit that is partitioned into smaller, equally-sized units Fractional unit = e.g., the fifth unit in 3 fifths denoted by the denominator 5 in 3 5

Suggested Tools & Representations

SPRINT State the missing factor. 10 = 5 x ___ 10 = 2 x ___ 6 x 4 = 4 x 2 x ___ 12 = 3 x 2 x ___ 20 = 5 x 2 x ___ 9 x 4 = 3 x 2 x ___ 9 x 4 = 3 x 3 x ___ 16 = 8 x ___ 16 = 4 x 2 x ___ 8 x 8 = 8 x 4 x ___ 9 x 9 = 3 x ___ x 3 8 x 3 = ___ x 6 16 x 2 = ___ x 4 2 x 18 = ___ x 9 28 x 2 = ___ x 8 24 x 3 = ___ x 9 6 x 8 = ___ x 12 27 x 3 = ___ x 9 12 x 6 = ___ x 8 54 x 2 = ___ x 12 9 x 13 = ___ x 39 8 x 8 = 2 x ___ 7 x 7 = ___ x 7

Skip Counting by 𝟏 𝟒 Hour Let’s count by ¼ hours. ¼ hour, 2 4 hour, 3 4 hour, 1 hour 1 ¼ hour, 1 2 4 hour, 1 3 4 hour, 2 hours 2 ¼ hours, 2 2 4 hours, 2 3 4 hours, 3 hours

Application Problem: 1 5 . 4 3 -1 2 - 2 8 2 0 0 . 7 - 2 0 5 15 kilograms of rice are separated equally into 4 containers. How many kilograms of rice are in each container? Express your answer as a decimal and as a fraction. 1 container 4 units = 15 kg 1 unit = 15 ÷ 4 = 3.75 = 3 75 100 1 5 . 4 3 -1 2 - 2 8 2 0 0 . 7 - 2 0 5 ? 15 kilograms Each container holds 3.75 kg rice.

Concept Development – Problem 1: Take your paper strip. Hold it horizontally. Fold it vertically down the middle. How many equal parts do you have in the whole? 2 What fraction of the whole is 1 part? 1 half = ½ Draw a line to show where you folded your paper and label each have ½, one out of 2 units. As you did in fourth grade, take about 2 minutes to make paper strips to also show thirds, fourths, and fifths.

Concept Development – Problem 1: Draw a number line in your journal that is a little longer than your paper strip. Use your strip as a ruler to mark zero and 1 above the line, 0 2 , 1 2 , 2 2 below the line. Make about an inch by inch square beneath your line. This is representing the same 1 whole as the number line. For today, show half by vertically dividing the square. Shade ½ on the left. Draw another square to the right of that one. Shade it in the same way to represent ½ . Partition it horizontally across the middle. What fraction is shaded now? ½ or 2 4

Concept Development – Problem 1: 1 2 = 1 group of two 2 group of two or 1 x 2 2 x 2 = 2 4 Explain how we have represented the equivalent fractions to your part. Show me 2 4 on the number line. It is the exact same number as 1 half, the exact same point on the number line. Work with a partner to draw another congruent square with 1 half shaded. This time partition it horizontally into 3 equal units (2 lines) and record the equivalent fraction as we did in the first example. Continue the pattern.

Concept Development – Problem 1:

Concept Development – Problem 2: Make fractions equal to 1 3 . Draw a line in your journal that is a little longer than your paper strip. Use your strip as a ruler and mark zero and 1 above the line, and 0 3 , 1 3 , 2 3 , 3 3 below the line. Work with your partner to make fractions that are equivalent to 1 3 and 2 3 .

Concept Development – Problems 2-3: Make fractions equal to 1 3 and 2 3 . Draw two lines in your journal that are a little longer than your paper strip. Use your strip as a ruler and mark zero and 1 above the lines, and 0 3 , 1 3 , 2 3 , 3 3 below the lines. Work with your partner to make fractions that are equivalent to 1 3 and 2 3 .

Concept Development – Problems 2-3:

Concept Development – Problem 4: Make fractions equal to 5 4 . Using the same procedure, write two fractions that are equivalent to 5 4 .

Activity Sheet Distribute the activity worksheet. Students work independently for 10 minutes. Debrief with the students by reviewing equivalent fractions.

Exit Ticket

HOMEWORK TASK Assign Homework Task. Due Date: ______________