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Grade 4 · Multiplication

Trail-map design: multiply every expanded place-value part

At a trail-map workshop, 2 identical supply sets each contain 731 map symbols. Change the controls and explain what the animation reveals.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Trail-map design: multiply every expanded place-value part. Hundreds product: 1,400. Tens + ones products: 62. Total product: 1,462731 × 2 = 1462700 × 2 = 140030 × 2 = 601 × 2 = 2Multiply every place-value part, then combine.
The quantities are invented for this investigation. Controls change the model rather than real-world records. Displayed decimals are rounded; whole-number counts are exact.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Hundreds product
1,400
Tens + ones products
62
Total product
1,462

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

At a trail-map workshop, 2 identical supply sets each contain 731 map symbols. Distributivity lets a multi-digit factor be split into hundreds, tens, and ones. Every part occurs in every set, so every place-value part must be multiplied by the same copy count. 700 × 2, 30 × 2, and 1 × 2 account for all 1462 objects.

A relationship to keep

731 × 2 = 1462

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Read the starting situation

    At a trail-map workshop, 2 identical supply sets each contain 731 map symbols. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Reveal the hundreds, tens, and ones products separately. Recombine those nonoverlapping contributions to recover the total. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    700 × 2, 30 × 2, and 1 × 2 account for all 1462 objects. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Trail-map design: use the original situation. At a trail-map workshop, 2 identical supply sets each contain 731 map symbols. How many objects would one additional identical set contribute, and what would the new total be?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

It contributes 731; the new total is 2193. A new copy repeats all the place-value parts.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 4 · Algebra

Multiply by expanding a three-digit number

Use partial products for a three-digit by one-digit product.