Free math simulations

Arithmetic series rectangles

Choose an arithmetic sequence and turn each term into a block. Fit the blocks together into a rectangle without breaking any of them. What does the rectangle tell you about the sum?

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About this simulation

Students type the first terms of an arithmetic sequence and each term becomes a block of unit squares. They fit the blocks together into a rectangle without breaking any, record its length, width and area, and use their results to build a rule for the sum. Then they test their rule with an odd number of terms.

Who it's for

MYP years 4–5 (ages 14–16), especially extended mathematics. Also a visual way into sequences and series at the start of DP.

How to use it

  1. Type the first four terms of an arithmetic sequence to make the blocks.
  2. Drag the blocks (or tap a block, then tap where it goes) to build a rectangle.
  3. Record the rectangle's length, width and area in the table.
  4. Look for a rule for the sum, then test it with an odd number of terms.
BranchNumerical and abstract reasoningTopicsSequences and seriesArithmetic sequencesArithmetic seriesPatterns
Your blocks will appear hereType the first four terms of a sequence to make them.
Drag a block to move it. Or tap a block, then tap where it should go (arrow keys move a tapped block).

My results