Explore · repeated fraction
Find 2 × 3/4 by thinking of 2 equal fractional groups.
Great Inheritance Mathematics Term A · Independent learning
Multiplying a Fraction by a Whole Number
Learning target: Interpret repeated fractional groups and simplify the product.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Prerequisite check (before instruction)
Attempt without help. A weak prerequisite signals review of 4A or 4B material, not a failed 5A lesson.
Show 3 × 1/4 using repeated addition.
Find 1/3 of 12 counters.
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
Write 3 × 1/4 as an addition sentence.
Understand the idea
Interpret repeated fractional groups and simplify the product.
A fraction multiplied by a whole number can mean equal fractional groups repeated. Three groups of 2/5 are 2/5 + 2/5 + 2/5 = 6/5. Simplify improper products as mixed numbers when requested.
Vocabulary focus: fraction of a quantity, overlapping partitions, reciprocal. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Confusing fraction times whole with fraction added to whole.
Model to study: Multiple repeated fractional strips.
Worked examples
Worked examples 1 · repeated fraction
Find 4 × 1/8 by thinking of 4 equal fractional groups.
Solution: 1/2
Why: Add 1/8 a total of 4 times, or multiply the numerator: (4×1)/8 = 1/2 = 1/2.
Worked examples 2 · repeated fraction
Find 6 × 4/6 by thinking of 6 equal fractional groups.
Solution: 4
Why: Add 4/6 a total of 6 times, or multiply the numerator: (6×4)/6 = 4 = 4.
Worked examples 3 · repeated fraction
Find 3 × 2/5 by thinking of 3 equal fractional groups.
Solution: 1 1/5
Why: Add 2/5 a total of 3 times, or multiply the numerator: (3×2)/5 = 6/5 = 1 1/5.
Check understanding
Check understanding 1 · repeated fraction
Find 5 × 3/5 by thinking of 5 equal fractional groups.
Check understanding 2 · repeated fraction
Find 4 × 4/8 by thinking of 4 equal fractional groups.
Guided practice
Guided practice 1 · repeated fraction
Find 4 × 2/4 by thinking of 4 equal fractional groups.
Guided practice 2 · repeated fraction
Find 2 × 1/5 by thinking of 2 equal fractional groups.
Guided practice 3 · repeated fraction
Find 4 × 3/4 by thinking of 4 equal fractional groups.
Independent practice
Independent practice 1 · repeated fraction
Find 4 × 1/5 by thinking of 4 equal fractional groups.
Independent practice 2 · repeated fraction
Find 2 × 4/8 by thinking of 2 equal fractional groups.
Independent practice 3 · repeated fraction
Find 3 × 1/6 by thinking of 3 equal fractional groups.
Independent practice 4 · repeated fraction
Find 4 × 2/3 by thinking of 4 equal fractional groups.
Independent practice 5 · repeated fraction
Find 6 × 2/4 by thinking of 6 equal fractional groups.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “2 × 2/3 = 8/3. I added one fraction only once.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 2 × 4/6 by thinking of 2 equal fractional groups.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Find 3 × 3/8 by thinking of 3 equal fractional groups.
Exit check
Exit check 1 · repeated fraction
Find 3 × 5/6 by thinking of 3 equal fractional groups.
Exit check 2 · repeated fraction
Find 5 × 2/8 by thinking of 5 equal fractional groups.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.