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

2. 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., = )
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., and 1 5 )
Unlike denominators = when the denominators in two or more fractions are different (e.g., and 1 7 )
Benchmark fractions = common fractions that you can compare other fractions against (e.g., 1 2, , , , 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

3. Suggested Tools & Representations

4. 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

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

6. 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 =
1 5 . 4 3
-1 2 2
0 0
. 7
- 2 0 5 ?
15 kilograms
Each container holds 3.75 kg rice.

7. 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.

8. 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, , , 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

9. 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 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.

10. Concept Development – Problem 1:

11. Concept Development – Problem 2:
Make fractions equal to
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 , , , below the line.
Work with your partner to make fractions that are equivalent to and

12. Concept Development – Problems 2-3:
Make fractions equal to and
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 , , , below the lines.
Work with your partner to make fractions that are equivalent to and

13. Concept Development – Problems 2-3:

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

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

16. Exit Ticket

17. HOMEWORK TASK
Assign Homework Task. Due Date: ______________