Grade 5 (age 10-11)

grade 5 Patterns and Correspondence

Patterns and Correspondence

Correspondence means that once one quantity is set, the other is fixed with it. If one pencil costs 500 won, three cost 1500 won, and as the count grows the price follows the same rule. Watch how much △ rises each time ○ goes up by 1, write the rule as △ = ○ × □, and the plotted points form a straight line. Change the multiplier and the addend and the table and graph fill in; change the price of one item and the cost by quantity appears.

Relation Between Two Quantities

🔗 When one changes, the other does too

①A pencil 500 won → 3 pencils 1500 won

②When one quantity is fixed, so is the other

③This relation is called "correspondence"

Build a Correspondence Table

Multiplier3

Add1

💡 Turn the rule into a formula!

①Find the rule in the table

②How much △ grows when ○ grows by 1

③If add is 2, then △ = ○×mul+2. Example: ○=3, mul=4, add=2 so △=14. The examples below only ask add 0: △=○×500

Real-life Correspondence

💡 What the 500 slider shows

①The price-each slider shows cost by quantity. Add is 0, so △=○×price

②Unlike the multiplier and add above, this step only changes a real-life price

③On the first screen 500 means 3 pencils cost 1500

Price each500 won

Summary

Correspondence

○ → △ (△ is determined by ○)

Each input gives one output

Find the Rule

△ = ○ × (mul) + (add)

Analyze differences to write the rule

Show as Graph

Plot the table on coordinates → see the rule

A straight line means constant difference

🎯 Key Points

①Correspondence: one quantity determines another

②Tables make rules visible

③A formula lets you find any value

④Price, distance, time are real-life examples

⑤Use both graph and table for clarity

Examples and Unit Test

Example 1

A pencil costs 500 won. How much for 3 pencils?

When the number of pencils (○) is fixed, the price (△) is also fixed; this is a correspondence.

Price = number × 500, so 3 × 500 = 1500 won.

▸ 1500 won

Correspondence: when one quantity is fixed, the other is determined.

Example 2

With a pencil at 500 won, let ○ be the number and △ the price. Write the rule as a formula.

When ○ increases by 1, △ increases by 500.

So the rule is △ = ○ × 500.

▸ △ = ○ × 500

See how much △ grows per +1 of ○ to write the rule as a formula.

Unit Test

In the rule △ = ○ × 500, what is △ when ○ = 5?

①505

②2500

③5500

④100

▸ ② 2500

Substitute ○ = 5 into △ = ○ × 500.

5 × 500 = 2500.

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Data Representation