What is this skill?
Multiplicative comparison is the fourth grade idea behind phrases like "5 times as many", "3 times as tall" and "4 times as much". It compares two amounts by how many copies of the smaller one fit into the bigger one, not by how much bigger it is. "Leo has 7 cards. Maya has 5 times as many" means Maya has five piles the size of Leo’s, which is 35 cards. Children also learn to write that comparison as an equation, 35 = 5 × 7, and to read an equation like 35 = 5 × 7 as the sentence "35 is 5 times as many as 7".
The unknown can be in any of three places: the bigger amount (multiply), the smaller amount ("Maya has 35 cards, which is 5 times as many as Leo has", so divide), or the number of times ("Maya has 35 and Leo has 7; how many times as many?", also divide). The practice mixes these with ordinary "more than" comparisons, so that your child has to decide each time whether the story adds a piece or makes copies, and then solve it.
Why it matters
"5 more than" and "5 times as many" sound very alike, and children often treat them the same way. Keyword lists make this worse: "times" seems to mean multiply, so "35 is 5 times as many as Leo has" becomes 35 × 5. Noticing which amount is the bigger one, and whether it is made of copies, is what protects against that.
The bar model makes the difference visible. For "more than", the longer bar is the shorter bar plus an extra piece. For "times as many", the longer bar is made of equal units, each the same size as the shorter bar. This picture of equal units is the bridge to scaling in fifth grade, where multiplying by a fraction can make something smaller, and to ratios in middle school.
Common mistakes
- Adding instead of multiplying, or the other way round. Ask your child to say the comparison in their own words: "Is it a few more, or is it a whole number of copies?"
- Multiplying when the bigger amount is already known. In "Noah’s tower is 72 centimeters tall, which is 9 times as tall as Mateo’s", the 72 is the bigger tower, so the answer is 72 ÷ 9.
- Writing the equation backward, such as 7 = 5 × 35. Checking whether the equation is true with real numbers is a quick fix.
- Losing track of who is who. Labelling each bar with a name before writing numbers keeps the story straight.
How to help at home
- Build with blocks or coins. Make a tower of 3, then show "3 more" and "3 times as many" side by side.
- Use prices at the store: "This costs $4. That one costs 3 times as much. How much is it?" Then ask the reverse question.
- Say an equation like 24 = 4 × 6 and ask your child for the sentence ("24 is 4 times as many as 6"), then go the other way.
- When your child answers, ask "is it bigger or smaller than the number you started with, and does that make sense?"
Worked examples
These are real questions from the Tutorsaurus times as many vs. more than practice, with the answers worked out.
Example 1
Kenji's block tower is 5 centimeters tall. Eli's block tower is 7 times as tall. How tall is Eli's block tower? What kind of story is this?
Choices: Times as many (× or ÷), More than (+ or −)
Answer: Times as many (× or ÷). This is a times-as-many compare story. 7 × 5 = 35.
Example 2
Zoe has 10 balloons. That is 5 times as many as Omar has. How many balloons does Omar have? Which number sentence matches the story?
Choices: 5 + 10 = ?, 5 × ? = 10, ? + 5 = 10, 5 × 10 = ?
Answer: 5 × ? = 10. 5 × 2 = 10 is true, and it follows the story. This is a times-as-many compare story. The word times is a clue, not a rule: 10 is the bigger amount, so divide. 10 ÷ 5 = 2.
Example 3
Ava has 84 more marbles than Eli. Ava has 125 marbles. How many marbles does Eli have?
Answer: 41. This is a compare story. The word more is a clue, not a rule: Ava has the bigger amount. 125 − 84 = 41.
Printable worksheet (PDF) — one page of times as many vs. more than problems from the same practice, easier ones first, with an answer key on page 2. Free to print, no sign-up. See all 4th grade math worksheets.