Add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator

Place value lets us split numbers into hundreds, tens and ones, regroup equal values and choose efficient addition or subtraction strategies.

Learning routine: Estimate → Partition → Regroup → Calculate → Check with inverse

Success looks like

• Partition numbers
• Regroup accurately
• Add three-digit numbers
• Subtract three-digit numbers
• Check with inverse

Success criteria:

• Partition numbers
• Regroup accurately
• Add three-digit numbers
• Subtract three-digit numbers
• Check with inverse

Key idea: Place value lets us split numbers into hundreds, tens and ones, regroup equal values and choose efficient addition or subtraction strategies.

Learning routine: Estimate → Partition → Regroup → Calculate → Check with inverse

partition

split a number into useful place-value parts

regroup

rename a quantity without changing its value

inverse

an operation that undoes another operation

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

• Content description: add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
• E1: using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written “jottings” to keep track of the numbers if necessary
• E2: using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations; for example, to calculate 214 + 325 representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones resulting in 5 groups of 100, 3 groups of 10 and 9 ones which is 539
• E3: choosing between standard and non-standard place value partitions to assist with calculations; for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850
• E4: solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 \space- \space395 adding 5 to both numbers to make 539 \space - \space400 = 139
• E5: justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems
• E6: applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week

Australian, Victorian and NSW alignment retained from the previous page

What is the big idea in this topic?

Place value lets us split numbers into hundreds, tens and ones, regroup equal values and choose efficient addition or subtraction strategies.

What routine should I use?

Estimate → Partition → Regroup → Calculate → Check with inverse

How do I know I am ready to move on?

You can partition numbers, regroup accurately, add three-digit numbers, subtract three-digit numbers, check with inverse and explain how your model or calculation supports the answer.

• Regrouping without equal exchange — Trade 10 ones for 1 ten or 10 tens for 1 hundred.
• Losing the adjustment — Compensation must be corrected at the end.
• No reasonableness check — Estimate before or after calculating.

1. Estimate 594 + 208, then calculate the exact answer and compare.

2. A student writes 268 + 157 = 315 because they added 8 + 7 as 5. Explain the regrouping error.

Review hint: Follow the routine “Estimate → Partition → Regroup → Calculate → Check with inverse” and use the worked model to check whether your answer is reasonable.

Place value lets us split numbers into hundreds, tens and ones, regroup equal values and choose efficient addition or subtraction strategies.

Learning routine: Estimate → Partition → Regroup → Calculate → Check with inverse

Success looks like

• Partition numbers
• Regroup accurately
• Add three-digit numbers
• Subtract three-digit numbers
• Check with inverse

Success criteria:

• Partition numbers
• Regroup accurately
• Add three-digit numbers
• Subtract three-digit numbers
• Check with inverse

• Australian Curriculum Version 9.0 — ACARA
• Victorian Curriculum — VCAA
• NSW Curriculum — NESA

Official curriculum sites are the source of record.

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