A little less prep. More room to teach.

LEARNING GOAL We are learning to recognize and create fractions that name the same amount. SUCCESS CRITERIA 1. I can represent equivalent fractions using equal-sized wholes. 2. I can create an equivalent fraction by multiplying the numerator and denominator by the same number. 3. I can explain why two fractions name the same amount. CURRICULUM CONNECTION Suggested connection: representing and comparing fractions. Verify the current Grade 4 expectations for your classroom before use; no official expectation has been supplied. MATERIALS & PREPARATION Paper, pencils and a whiteboard. Prepare two equal-sized paper rectangles. Worksheets can be printed, projected or copied onto paper. MINDS ON · 10 MINUTES Draw two equal-sized rectangles. Divide the first into 2 equal parts and shade 1. Divide the second into 4 equal parts and shade 2. Ask: “What changed? What stayed the same?” Model the explanation: “The pieces became smaller, but the shaded amount stayed the same. One half and two fourths are equivalent.” Emphasize that the wholes must be the same size. ACTION · 30 MINUTES First 10 minutes: Have pairs fold or draw equal-sized rectangles to show 1/2, 2/4 and 4/8. Ask them to explain why doubling both numbers keeps the shaded amount unchanged. Next 15 minutes: Students complete the core worksheet. Offer the supported version with prompts, or the extension version for deeper reasoning. These are alternative routes to the same goal, not a sequence everyone must finish. Final 5 minutes: Compare two solutions to the snack-sharing problem. Listen for explanations about equal-sized wholes, rather than “the numbers look similar.” CONSOLIDATION · 10 MINUTES Spend 5 minutes discussing the misconception 1/2 = 2/3. Draw both using equal-sized wholes and ask what went wrong. Use the remaining 5 minutes for the exit ticket. Collect explanations as well as numerical answers. ACCESS & SUPPORT Use large, uncluttered fraction models. Read instructions aloud and allow oral explanations or drawings. Sentence starter: “These fractions are equivalent because…” Avoid relying on colour alone to distinguish parts. ASSESSMENT & NEXT STEPS Check whether students keep the whole the same size and change both numerator and denominator by the same factor. If needed, revisit folding and partitioning before symbolic rules. Extend by asking students to create three names for the same fraction.

EQUIVALENT FRACTIONS · CORE PRACTICE Name: ____________________ Date: ____________________ Use drawings or number patterns. When you draw fractions, keep the wholes the same size. 1. Write two different fractions equivalent to 1/2. Draw a model to show one of your answers. ____________________________________________________ ____________________________________________________ 2. Complete the equality: 3/4 = ___/8. Explain what happened to both numbers. ____________________________________________________ ____________________________________________________ 3. Complete the equality: 2/3 = 6/___. Show how you know. ____________________________________________________ ____________________________________________________ 4. Are 2/4 and 3/6 equivalent? Draw equal-sized wholes or explain your reasoning. ____________________________________________________ ____________________________________________________ 5. Two identical snack bars are shared. One is cut into 8 equal pieces and 4 are eaten. The other is cut into 6 equal pieces and 3 are eaten. Was the same amount eaten from each bar? Explain. ____________________________________________________ ____________________________________________________

EQUIVALENT FRACTIONS · STEP BY STEP Name: ____________________ Date: ____________________ REMEMBER The denominator tells how many equal parts make the whole. The numerator tells how many parts we are counting. WORKED EXAMPLE 1/2 = 2/4. Multiply the top number by 2 and the bottom number by 2. The number of pieces changes, but the amount stays the same. 1. Draw a rectangle split into 4 equal parts. Shade 2 parts. The shaded fraction is 2/4. It is also ___/2 of the whole. ____________________________________________________ ____________________________________________________ 2. Fill in the missing number: 1/3 = ___/6. Think: 3 × 2 = 6, so 1 × 2 = ___. ____________________________________________________ 3. Draw two equal-sized rectangles. Shade 1/2 of one and 3/6 of the other. Complete: “These fractions are equivalent because…” ____________________________________________________ ____________________________________________________

EQUIVALENT FRACTIONS · GO DEEPER Name: ____________________ Date: ____________________ Show your reasoning with words, diagrams or calculations. 1. Write a fraction equivalent to 2/3 with a denominator of 18. Explain the relationship between the two fractions. ____________________________________________________ ____________________________________________________ 2. A classmate says 3/4 = 9/12. Explain why this works. Then create a different equivalent fraction and show the rule you used. ____________________________________________________ ____________________________________________________ 3. A classmate adds 3 to both numbers and writes 1/2 = 4/5. Explain why this does not work. Use equal-sized wholes to support your explanation. ____________________________________________________ ____________________________________________________

BEFORE YOU GO · EXIT TICKET Name: ____________________ Date: ____________________ 1. Complete: 1/2 = ___/6. ____________________________________________________ 2. Are 2/3 and 4/6 equivalent? Explain or draw a model using equal-sized wholes. ____________________________________________________ ____________________________________________________

TEACHER COPY · ANSWER KEY CORE WORKSHEET 1. Examples: 2/4, 3/6 or 4/8. Accept any two correct equivalent fractions. Drawings should show equal-sized wholes with one half shaded. 2. 6/8. Both numerator and denominator are multiplied by 2. 3. 6/9. Both numerator and denominator are multiplied by 3. 4. Yes. Both represent 1/2 of the same-sized whole. 5. Yes. 4/8 = 1/2 and 3/6 = 1/2. Each identical bar has half eaten. SUPPORTED WORKSHEET 1. 1/2. The model should have 2 of 4 equal parts shaded. 2. 2/6; the second blank is 2. 3. Drawings should show the same shaded amount. Sample response: “Both show half of the same-sized whole.” EXTENSION WORKSHEET 1. 12/18. Multiply both numbers in 2/3 by 6. 2. Multiply both numbers by 3 to get 9/12. Other examples include 6/8 or 12/16 with a correct explanation. 3. Adding the same number does not preserve the ratio. 1/2 is one half, while 4/5 is more than one half. Accept accurate equal-whole diagrams demonstrating the difference. EXIT TICKET 1. 3/6. 2. Yes. Multiplying both numbers in 2/3 by 2 gives 4/6. Accept an accurate drawing or equivalent explanation. LOOK FOR Equal-sized wholes, equal-sized parts within each whole, and the same multiplicative change to numerator and denominator. Revisit visual models if a student adds the same amount to both numbers.