Compare Expressions Without Unneeded Arithmetic

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: Compare 4×(125+39) with 125+39.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Expression structure can show a size relationship directly. Three times a sum is three copies of that entire sum, even when its numbers are large. This is different from adding three to the sum. When the underlying sum is positive, three copies are three times its value.

Identify the repeated or scaled quantity in both supplied expressions. Use the multiplier relationship instead of evaluating the inner sum if the question asks only for relative size. Explain the scope using parentheses.

Treat the identical grouped part as one named quantity. Times as large and more are different relationships. Label the repeated grouped sum S and compare the multiples of S.

1. Label the repeated grouped sum S and compare the multiples of S.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Identify the repeated or scaled quantity in both supplied expressions.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Compare 6×(408+27) with 2×(408+27). Expected: first is three times the second.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.