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Grade 4 · Factors

Book-drive planning: test divisibility by making full groups

At a book drive, 31 donated books are packed in groups of exactly 3. 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
Book-drive planning: test divisibility by making full groups. Final complete groups: 10. Final remainder: 1. Distributed so far: 031 = 10 × 3 + 1A remainder is not another complete group.
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.

Final complete groups
10
Final remainder
1
Distributed so far
0

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 book drive, 31 donated books are packed in groups of exactly 3. Division by group size asks how many complete groups fit. A candidate factor divides a whole number exactly only when no objects remain outside the complete groups. 10 full groups fit and 1 remain. Therefore 3 is not a factor of 31.

A relationship to keep

31 = 10 × 3 + 1

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 book drive, 31 donated books are packed in groups of exactly 3. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Watch the group colors separate successive groups of the specified size. A final incomplete group is a remainder, not another complete package. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    10 full groups fit and 1 remain. Therefore 3 is not a factor of 31. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Book-drive planning: use the original situation. At a book drive, 31 donated books are packed in groups of exactly 3. Can every object be packed into complete groups of 3, with none left over?

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

Compare your explanation

No. 10 groups use 30, leaving 1.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 4 · Algebra

Find every factor pair

List whole-number factor pairs systematically.