Number Facts and Mental Maths Strategies

Active learning helps students internalize number facts and mental strategies by connecting abstract ideas to movement, discussion, and visuals. For this topic, movement-based games and partner talks make recall faster and more flexible than worksheets alone. Students need to hear, see, and verbalize the reasoning behind strategies to move beyond rote memory.

• 2nd Class
• Mathematical Explorers: Building Foundations
• 4 activities
• 15 min–30 min

Learning Objectives

1. Calculate the sum of two two-digit numbers without renaming using place value partitioning.
2. Explain how knowing addition facts to 20 supports mental calculation of two-digit sums.
3. Identify and apply strategies such as making ten or counting on to solve two-digit addition problems.
4. Demonstrate the connection between known addition facts and the process of adding tens and ones separately.

Simulation Game

⏱ 20 min·Pairs

Simulation Game: Doubles Dash

Prepare cards with doubles facts to 20 and near-doubles. Pairs take turns drawing a card, solving mentally, and racing to write the answer before a 30-second timer. Switch roles after five cards; discuss any errors as a pair to refine strategies.

Prepare & details

What addition and subtraction facts do you already know by heart?

Facilitation Tip: During Doubles Dash, circulate and model calling out doubles facts aloud with students to keep the pace lively and accurate.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Peer Teaching

⏱ 25 min·Pairs

Partner Strategy Share: Making Ten

Give pairs two-digit addition problems without renaming, like 34+16. One student models partitioning on a mini-whiteboard (30+10=40, 4+6=10), the partner repeats with a new problem. Pairs then invent their own problems to swap and solve.

Prepare & details

How can knowing doubles or near-doubles help you add quickly?

Facilitation Tip: During Partner Strategy Share: Making Ten, provide sentence starters like 'I made ten by...' to guide clear explanations.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Peer Teaching

⏱ 30 min·Whole Class

Whole Class: Fact Family Bingo

Distribute bingo cards with facts to 20 and strategy clues (e.g., 'double 7'). Call out verbal problems; students mark answers mentally and justify to a neighbor. First full row wins a group cheer; review strategies class-wide.

Prepare & details

Can you use a mental maths strategy to find the answer to a two-digit addition or subtraction?

Facilitation Tip: During Fact Family Bingo, allow students to use mini whiteboards to jot down facts quickly before marking their cards.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Peer Teaching

⏱ 15 min·Individual

Individual: Strategy Number Line Hunt

Students draw a number line from 0-100 and solve 10 two-digit additions without renaming by jumping tens then ones. They note the strategy used (e.g., doubles) beside each. Share one favorite with the class.

Prepare & details

What addition and subtraction facts do you already know by heart?

Facilitation Tip: During Strategy Number Line Hunt, ask students to mark their starting point and jumps with different colors to track their thinking.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Teaching This Topic

Teach number facts as a network of connected ideas rather than isolated bits of information. Use games to build speed and accuracy, and class discussions to highlight patterns like how near-doubles relate to doubles. Avoid rushing students to written algorithms before they can explain their mental steps. Research shows that students who verbalize strategies during partner work develop stronger number sense than those who only write answers.

What to Expect

Students should confidently recall addition and subtraction facts to 20, explain at least two mental strategies they use, and solve two-digit sums without counting every single number aloud. They should also compare their methods with peers and adjust their thinking based on feedback. Success looks like students choosing strategies that make sense to them and using them efficiently.

Watch Out for These Misconceptions

Common Misconception

During Doubles Dash, watch for students who always start adding from the ones digit mentally, even when it slows them down.

What to Teach Instead

Remind students to start with the larger number and use doubles or near-doubles from there. Ask them to explain their first step aloud to their partner before racing ahead.

Common Misconception

During Partner Strategy Share: Making Ten, watch for students who treat number facts as isolated facts without connections to other strategies.

What to Teach Instead

Guide them to link their facts to doubles or near-doubles during the share. For example, if they say '7 + 3 = 10,' ask how that helps with '17 + 3' or '7 + 13.'

Common Misconception

During Strategy Number Line Hunt, watch for students who rely on counting every single number rather than using jumps or partitioning.

What to Teach Instead

Ask them to circle the larger number and draw a jump first, then add the rest. Model this on their number line with a different color.

Assessment Ideas

Quick Check

After Doubles Dash, present a problem like 34 + 25 on the board and ask students to write the answer and one strategy they used on a sticky note. Collect these to check who can calculate correctly and name a strategy.

Discussion Prompt

During Partner Strategy Share: Making Ten, pose the question, 'How does knowing that 6 + 6 = 12 help you figure out 26 + 6?' Listen for explanations that mention adding the tens first or using doubles.

Exit Ticket

After Strategy Number Line Hunt, give each student a card with a problem such as 41 + 37. Ask them to write the answer and draw a small number line showing how they partitioned the sum using place value.

Extensions & Scaffolding

• Challenge students to create their own two-digit addition problems and explain the strategy they used to a partner, using a timer to track how quickly they solve it.
• Scaffolding: Provide a partially completed number line with some steps filled in for students who struggle with partitioning.
• Deeper exploration: Ask students to invent a new mental strategy for two-digit addition and teach it to the class during a follow-up session.

Key Vocabulary

Place Value	The value of a digit in a number, based on its position. For example, in 23, the 2 represents 2 tens and the 3 represents 3 ones.
Partitioning	Breaking a number down into smaller parts, often based on place value. For example, partitioning 23 into 20 and 3.
Addition Facts	Basic addition combinations, typically up to 20, that students should know by heart, such as 7 + 5 = 12.
Mental Maths Strategy	A specific technique used to solve a calculation in one's head, such as counting on or making ten.