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Fraction Classroom · 2.3.0 · Student pages

Distinguish times as many from more than

Use equal comparison units to separate multiplicative comparisons from additive differences and identify the unknown quantity.

Anonymous group code: __________   Date: __________

Lee has one group of 5 counters. Sam has three equal groups of 5, so the comparison is multiplicative.Reference: 5 counters53 times as many555
Lee has one group of 5 counters. Sam has three equal groups of 5, so the comparison is multiplicative.

Build the idea

model. Lee has 5 counters. Sam has 3 times as many counters as Lee. How many counters does Sam have?

  1. Identify the reference quantity: Lee's five counters make one comparison unit. The phrase three times as many describes how many copies of that unit to use.
  2. Draw three equal boxes for Sam, each containing five. Keep the box size consistent so every copy represents the same count.
  3. Multiply 3 × 5 = 15. Contrast this with three more than five, which would be 5 + 3 = 8 and would describe a different relationship.
  4. Check the comparison by division: 15 ÷ 5 = 3. The quotient counts copies of Lee's amount, not extra counters beyond Lee's set.

Worked example: 15 counters. One comparison unit is Lee's set of 5; Sam has three copies of that entire amount.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. One tray holds 6 counters. Another holds 4 times as many. How many counters are in the other tray?

p2. One collection has 21 counters and another has 7. How many times as many counters are in the first collection?

p3. A collection of 32 counters is 4 times as large as a smaller collection. How many counters are in the smaller collection?

e1. A red ribbon is 6 cm long. A blue ribbon is 5 times as long. Find the blue length in cm and explain why 11 cm would answer a different question.

Transfer the idea

transfer. For a reference amount of 4, compare three times as many with three more. State both results and describe what the 3 counts.