Mathematics · Year 2 · Additive Thinking and Strategies · Term 2

Mental Math Strategies for Addition

Students develop and apply mental strategies like doubles, near doubles, and making to ten for addition.

• ACARA Content Descriptions
• AC9M2N03

About This Topic

Year 2 students build mental math fluency for addition through strategies like doubles (5+5=10), near doubles (6+5=11 as double 5 plus 1), and making to ten (8+6=14 as 8+2=10 then +4). These methods, aligned with AC9M2N03, help compute facts to at least 100 efficiently without counting all or using fingers every time. Students practice partitioning numbers flexibly, such as seeing 9+7 as (10-1)+7 or 9+(10-3).

In the Additive Thinking and Strategies unit, key questions guide learning: compare strategy efficiency for problems like 13+8, justify making to ten's power for bridging to tens, and predict suitable strategies for facts like 12+9. This develops deeper number sense, logical reasoning, and confidence in choosing tools for tasks.

Active learning benefits this topic greatly. Partner games and group challenges let students test strategies on real problems, discuss efficiencies, and refine their thinking collaboratively. Hands-on tools like number lines or ten-frames make abstract ideas concrete, while sharing solutions builds a classroom community of problem solvers.

Key Questions

1. Compare the efficiency of different mental math strategies for a given addition problem.
2. Justify why 'making to ten' is a powerful mental strategy.
3. Predict which mental strategy would be most suitable for various addition facts.

Learning Objectives

• Compare the efficiency of 'doubles', 'near doubles', and 'making to ten' strategies for solving addition problems.
• Explain the process of 'making to ten' to bridge a number to the nearest multiple of ten.
• Calculate sums using 'doubles' and 'near doubles' strategies.
• Apply the 'making to ten' strategy to solve addition facts involving numbers that do not immediately sum to ten.
• Justify the selection of a specific mental math strategy for a given addition problem.

Before You Start

Number Bonds to Ten

Why: Students need a solid understanding of how numbers combine to make ten to effectively use the 'making to ten' strategy.

Counting On

Why: This foundational strategy helps students understand the concept of addition and provides a basis for more advanced mental strategies.

Key Vocabulary

Doubles	Adding a number to itself, such as 7 + 7. This strategy uses known facts to solve similar problems.
Near Doubles	Using a known doubles fact to solve a problem where the addends are close, like 7 + 8, by thinking of it as 7 + 7 + 1.
Making to Ten	A strategy where one addend is broken apart to complete a ten with the other addend, for example, 8 + 5 becomes 8 + 2 + 3, which equals 10 + 3.
Partitioning	Breaking a number into smaller parts to make calculations easier, such as breaking 6 into 2 and 4 to help make a ten.

Watch Out for These Misconceptions

Common Misconception

Always count on from the larger number.

What to Teach Instead

This works but slows fluency for larger facts. Active pair discussions reveal faster options like making to ten, as students time each method and compare results, building preference for efficiency.

Common Misconception

Doubles only work for even addends.

What to Teach Instead

Students overlook doubles with odds via near doubles, like 7+7=14 then adjust. Group games with varied cards expose this, prompting peer explanations that clarify adjustments during play.

Common Misconception

Making to ten is just for numbers near 10.

What to Teach Instead

It applies broadly, like 13+8 as (10+3)+8. Strategy stations let students experiment across ranges, correcting through trial and shared successes.

Active Learning Ideas

Partner Strategy Duels: Addition Showdown

Pairs draw cards with sums like 9+6 and race to solve using different strategies, then explain their choice to partners. Switch roles after each round and record the fastest method. Debrief as a class on patterns.

30 min·Pairs

Stations Rotation: Strategy Workshops

Set up stations for doubles (domino matching), near doubles (dice rolls adjusted by 1), making to ten (ten-frame cards), and mixed practice (whiteboard challenges). Groups rotate every 7 minutes, noting strategy use in journals.

45 min·Small Groups

Whole Class Number Talks: Strategy Shares

Pose problems like 14+7 on the board. Students signal thinking with fingers (1 for doubles, 2 for near doubles, 3 for making to ten), then share and justify aloud. Tally most efficient strategies on a chart.

20 min·Whole Class

Individual Strategy Hunts: Fact Families

Students get fact family sheets (e.g., around 10+5) and circle numbers to make tens, draw doubles, or note near doubles. They solve 10 problems and pick their top strategy for each.

15 min·Individual

Real-World Connections

• Cashiers at a grocery store use mental math strategies to quickly calculate the total cost of items, especially when dealing with prices that are close to round numbers. For example, they might use 'making to ten' to add items priced at $8 and $5.
• Construction workers often estimate quantities and sums on the job. A carpenter might mentally add the lengths of two pieces of wood, using strategies like 'near doubles' if the lengths are similar, to determine if they fit a required measurement.

Assessment Ideas

Quick Check

Present students with a list of addition problems (e.g., 7+7, 6+7, 8+5, 9+4). Ask them to write the strategy they used for each problem and the answer. For example, for 8+5, they might write 'making to ten' and 13.

Discussion Prompt

Pose the problem: 'Sarah solved 9 + 4 by thinking 9 + 1 + 3. Ben solved it by thinking 10 + 4 - 1. Who used 'making to ten' and why is that strategy helpful?' Facilitate a class discussion comparing their approaches.

Exit Ticket

Give each student a card with an addition problem, such as 12 + 5. Ask them to write down two different mental strategies they could use to solve it and state which strategy they think is most efficient and why.

Frequently Asked Questions

How do you teach making to ten in Year 2?

Model partitioning: for 9+4, add 1 to 9 for 10, then add 3 more. Use ten-frames or drawings to visualize. Practice with flashcards where students snap fingers to bridge to ten, then compute. Reinforce in daily warm-ups with mixed facts to build automaticity.

What are effective near doubles strategies?

Near doubles build on known doubles: 6+5 as double 5 (10) plus 1 (11), or 8+7 as double 7 (14) plus 1 (15). Introduce with visuals like connecting cubes in pairs. Games where students adjust doubles by 1 or 2 solidify this, linking to doubles facts.

How does active learning support mental math strategies?

Active approaches like partner duels and number talks engage students in applying, comparing, and justifying strategies dynamically. Collaborative challenges reveal inefficiencies in counting all, while sharing builds collective knowledge. This hands-on practice transfers to independent problem-solving, making fluency fun and memorable.

How to differentiate for students struggling with addition strategies?

Provide concrete tools like counters or number lines initially, then fade to mental. Pair stronger peers for modeling in duels. Offer strategy mats with visuals for reference. Track progress with personal goal charts, celebrating small wins to boost confidence.