Growing pattern builder

What the pattern builder does

A growing pattern changes by the same amount from one figure to the next, like 3, 5, 7, 9. In Build mode you choose how many tiles are added each time (1 to 4) and how many tiles stay the same in every figure (from −2 to 5). The tiles that grow are blue and sit in rows that get one tile longer with each figure; the tiles that stay are red and sit in a column on the left. A negative number of tiles that stay shows as dashed tiles taken away.

The table lists the tiles in figures 1 to 5 and figure 10, and the readout gives the rule, such as 2n + 1, plus figures 10 and 100. In Mystery mode the colors are hidden: you predict figure 4, then figure 10, then choose the rule from four options, and only then do the colors appear.

Why tiles help with sequences

Students often find the term-to-term rule (add 2 each time) but get stuck on figure 100, because adding 2 a hundred times is slow. Seeing the figure as rows of n tiles plus a fixed group shows where 2n + 1 comes from: two rows of n, plus 1. Once students can see the structure, predicting figure 10 or figure 100 becomes multiplying instead of counting on. Color-coding the part that grows and the part that stays makes the two numbers in the rule visible.

Common mix-ups

• Doubling figure 5 to get figure 10. For 2n + 1, figure 5 has 11 tiles but figure 10 has 21, not 22, because the extra 1 is not doubled.
• Writing the rule as n + 2 because the pattern adds 2 each time. The number added each time goes in front of n.
• Using figure 1 as the number in front of n. For 3, 5, 7, the rule is 2n + 1, not 3n.
• Thinking every pattern starts at figure 0. Here the first figure is figure 1.

A 10-minute pattern lesson

• In Build, show figures 1 to 4 for 2n + 1 with the readout covered.
• Ask students to describe what they see changing and what stays the same.
• Ask for figure 10 and how they worked it out, then turn on Show figure 10.
• Switch to Mystery and solve one pattern together.
• Challenge: find a pattern where figure 100 has 301 tiles.

Where it fits by grade

• Grades 4 and 5: generate patterns that follow a rule and notice features of the pattern (4.OA.C.5, 5.OA.B.3).
• Grade 6: describe how one quantity depends on another with an equation and a table (6.EE.C.9).
• Grade 8: build a function to model a linear relationship and find the rate of change and initial value (8.F.B.4).
• England: Year 6 generates and describes linear number sequences, and Key Stage 3 finds the nth term of linear sequences.

Learning more

Times tables and solving equations are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Lessons draw diagrams live from the numbers in each question, and the AI tutor asks guiding questions when a pattern is hard to see.