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Grade 5 · Patterns

Community-park layout: predict an additive number pattern

A planning table for a community-park design begins at 7, adds 7 each time, and lists 10 terms. 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
Community-park layout: predict an additive number pattern. Terms revealed: 0. Added each time: 7. Term 10: 70Start 7 · add 7 each time7142128354249566370Term 10 uses 9 additions, not 10.
This investigation explicitly uses an additive rule. A finite list alone can fit many rules, so the stated starting value and constant increment determine the continuation.

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.

Terms revealed
0
Added each time
7
Term 10
70

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.

A planning table for a community-park design begins at 7, adds 7 each time, and lists 10 terms. An additive pattern has a constant difference between neighboring terms. The first term already exists, so reaching term n requires n minus one additions, not n additions. Term 10 is 70, after 9 increments of 7. A different starting value shifts every term by the same amount.

A relationship to keep

Term n = 7 + (n − 1) × 7

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

    A planning table for a community-park design begins at 7, adds 7 each time, and lists 10 terms. 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 terms from left to right. Compare consecutive differences before predicting the final term from the rule. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    Term 10 is 70, after 9 increments of 7. A different starting value shifts every term by the same amount. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Community-park layout: use the original situation. A planning table for a community-park design begins at 7, adds 7 each time, and lists 10 terms. What is the next term after the displayed 10 terms?

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

Compare your explanation

77. Add 7 once more to 70.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 5 · Algebra

Compare two rules in a table

Relate outputs of two multiplication patterns.