Multiplicative comparisons

What does “times” compare?

Read a multiplication equation as more than one numerical comparison.

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8 practice questions · Optional read aloud · Thinking pad

Let’s understand the idea.

  1. Mia has 9 pots. Sam has 3 times as many. Give Sam three groups of 9 pots: 9 + 9 + 9 = 27. Three more pots would give 9 + 3 = 12 instead.
  2. Read what the question asks you to find: one person's amount, the other person's amount, or how many equal groups connect them. Keep names and units with the numbers.
  3. Write n for the missing number. Multiply to find the total of equal groups. Divide a known total to find one group's amount or the number of groups. Check by multiplying back.
  4. Mathematical names: the amount we copy is the reference amount; the number of copies is the multiplier. In the pots example, these are 9 pots and 3 groups.
  5. Change the pots or the number of groups in the experiment. Compare adding individual pots with adding whole groups. Empty groups still contain zero pots, and one group keeps its original amount.

Something to notice

Observe unscaffolded explanations, student-made drawings and unfamiliar contexts. Multiple-answer questions check all valid numerical interpretations or equivalent comparison equations. The planner separately checks the requested role, a valid relationship equation and the numerical answer; the independent transfer lesson removes planning choices. Fixed-scale tapes and original labels preserve quantity meanings. Whole-number authoring/control bounds do not define the full standard; completion is not mastery, retention or proof of independent estimation.

Try it. Change it. Explain it.

Open the lesson to use its pictures and controls. In How it works, connect the picture to the idea. In Play & discover, change the quantities and notice what stays the same. In Your turn, answer questions and use the explanation to check your reasoning.

You can ask for help, draw on the thinking pad, or listen to the question and answer options. Progress distinguishes independent work from work completed with help.

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Curriculum connection

Grade 4 · 4.OA · US Common Core

4.OA.A.1

This lesson is mapped to these standards. A completed activity is practice evidence, not a claim of mastery. Content is checked against the linked official standards and its mathematical models are tested.

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