Grade 5 › G5U01 Place Value

Grade 5 › G5U01 Place Value › L2
GRADE 5 · ALBERTAOUTCOME AB-G5-5N1

L2 · The value of each digit; composing numbers many ways

Learning goal

“I can write a number in expanded form, build a number back from its expanded form, and compose the same number in different ways by trading between places - including decimals to thousandths.”

Expanded form — a number written as the sum of the values of its digits: 4,382 = 4,000 + 300 + 80 + 2.
Standard form — the usual way of writing a number with digits: 4,382.
Compose — to build a number up from parts, e.g. 30 tens compose 300.
Decompose — to break a number into parts, e.g. decomposing 300 into 30 tens.
Worked example

Write 6,304,518 in expanded form. Step 1 (digit by digit, left to right): 6 is 6,000,000; 3 is 300,000; 0 - skip (a zero digit adds nothing); 4 is 4,000; 5 is 500; 1 is 10; 8 is 8. Step 2 (write the sum): 6,304,518 = 6,000,000 + 300,000 + 4,000 + 500 + 10 + 8. Step 3 (refold to check): 6,000,000 + 300,000 = 6,300,000; + 4,000 = 6,304,000; + 500 = 6,304,500; + 10 = 6,304,510; + 8 = 6,304,518. The zeros in the number are the places that contribute no addend - but they still hold their columns in standard form.

Check yourself — explain it

The zero in 6,304,518 produces no addend in expanded form because...

Paired problem — example still visible

Write 2,450,706 in expanded form -> 2,000,000 + 400,000 + 50,000 + 700 + 6

Faded completion — last step is yours

"9,000,000 + 80,000 + 300 + 5 = ___" -> 9,080,305

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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