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Grade 4 · Multiplication

Food-bank packing: multiply every expanded place-value part

At a food-bank packing station, 5 identical supply sets each contain 351 food packets. 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
Food-bank packing: multiply every expanded place-value part. Hundreds product: 1,500. Tens + ones products: 255. Total product: 1,755351 × 5 = 1755300 × 5 = 150050 × 5 = 2501 × 5 = 5Multiply 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
1,500
Tens + ones products
255
Total product
1,755

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 food-bank packing station, 5 identical supply sets each contain 351 food packets. 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. 300 × 5, 50 × 5, and 1 × 5 account for all 1755 objects.

A relationship to keep

351 × 5 = 1755

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 food-bank packing station, 5 identical supply sets each contain 351 food packets. 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

    300 × 5, 50 × 5, and 1 × 5 account for all 1755 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.

Food-bank packing: use the original situation. At a food-bank packing station, 5 identical supply sets each contain 351 food packets. 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 351; the new total is 2106. 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.