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Lesson · Grade 4 · Mathematics

From a pattern to a table of values

  • Grade 4
  • Mathematics
  • 1 min 14 s
  • British Columbia
  • BC4-MA-19

A growing pattern of toothpick squares is counted one toothpick at a time into a table of values, giving 4, 7 and 10 toothpicks for Figures 1 to 3. The table shows the count goes up by 3 each time because each new square adds a top, a bottom and a side, so adding 3 twice more shows that Figure 5 needs 16 toothpicks.

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In one sentence

The question this lesson answers

Here is a growing pattern made of toothpicks. Each figure has one more square than the one before.

How many toothpicks will Figure 5 need? A table of values will help us find out.

Transcript

What the lesson says

Here is a growing pattern made of toothpicks. Each figure has one more square than the one before.

How many toothpicks will Figure 5 need? A table of values will help us find out.

Make a table with two rows: the figure number, and the number of toothpicks.

Count the toothpicks in each figure. Figure 1 has 4 toothpicks.

Figure 2 has 7 toothpicks.

Figure 3 has 10 toothpicks.

Now look at how the number of toothpicks changes from one figure to the next.

It goes up by 3 each time, because each new square adds 3 toothpicks: a top, a bottom and a side.

To continue the table, keep adding 3.

Figure 4 needs 10 plus 3, which is 13 toothpicks.

Figure 5 needs 13 plus 3, which is 16 toothpicks.

So Figure 5 needs 16 toothpicks.

To turn a pattern into a table of values, count each figure, write the counts in order, and look at how they change.

Curriculum

Where this fits

British Columbia, Grade 4

Mathematics, Patterns and algebra: increasing and decreasing patterns, using tables and chartsBC4-MA-19

Previous: Increasing and Decreasing Patterns: A Start Number and a RuleNext: Finding the Number in the Box

British Columbia, Grade 5

Mathematics, Patterns and algebra: rules for increasing and decreasing patterns with words, numbers, symbols, and variablesBC5-MA-23

Previous: The Start and the Change: Writing Pattern RulesNext: Solving One-Step Equations

British Columbia, Grade 6

Mathematics, Patterns and algebra: increasing and decreasing patterns, using expressions, tables, and graphs as functional relationshipsBC6-MA-24

Previous: Increasing and Decreasing Patterns: Find What Changes Each StepNext: Finding the rule from a table

British Columbia, Grade 7

Mathematics, Patterns and algebra: discrete linear relations, using expressions, tables, and graphsBC7-MA-34

Next: Finding the rule from a table

This lesson is also listed in Grade 5, Grade 6 and Grade 7.

The outcomes and strands follow the British Columbia curriculum.

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