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Grade 6 · Ratios

Robot controller: Build equivalent batches

Robot controller investigation: build equivalent batches. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

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

Watch the relationship

Paused
Robot controller: Build equivalent batches. Complete copies shown: 1. First quantity: 2. Second quantity: 3. Ratio first/second: 0.667Equivalent batches: 1 completeFirst quantity: 2Second quantity: 3One batch is 2 : 3
Batch counts are whole numbers. Quantities are scalable mathematical amounts; no claim is made that a fractional physical object can be manufactured. Both comparison bars use the same unit scale.

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.

Complete copies shown
1
First quantity
2
Second quantity
3
Ratio first/second
0.667

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.

Equivalent ratios multiply both quantities by the same factor. Building complete copies makes that requirement visible: multiplying just one quantity changes the mixture. A part-to-part ratio is different from either part as a fraction of the combined total. This investigation begins with first quantity per batch = 2; second quantity per batch = 3; final complete batches = 2. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

a : b = ka : kb

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

  1. STEP 1

    Represent the given quantities

    Read the two quantities in one complete batch and preserve their order when naming the ratio.

  2. STEP 2

    Follow the changing model

    Watch whole batches appear. Each copy contributes the same a and b, so both cumulative amounts grow together.

  3. STEP 3

    Check and explain the relationship

    Divide the two totals to check the unchanged ratio; use a+b as the denominator only when asking for a share of the whole.

Your turn to explain

Make a prediction. Test your reasoning.

Robot controller: A batch uses 2 units of the first ingredient and 3 of the second. Find both totals for 2 batches.

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

Compare your explanation

4 and 6 units; dividing the totals gives the original ratio 2:3.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 6 · Algebra

Build a table of equivalent ratios

Scale both entries of a ratio by a common factor.