Mathematics · Year 1 · Additive Reasoning · Autumn Term

Adding by Counting On (to 20)

Extending counting on strategies to solve addition problems with sums up to 20.

• National Curriculum Attainment Targets
• KS1: Mathematics - Addition and Subtraction

About This Topic

Adding by counting on builds fluency in mental addition for sums up to 20. Children start from the larger addend and count forward by the smaller one, such as solving 12 + 3 by saying twelve, thirteen, fourteen, fifteen. This strategy aligns with KS1 standards for addition and subtraction, extending prior counting skills into efficient problem-solving within the Additive Reasoning unit.

Students construct problems like 14 + 2, compare counting on to number bonds, and justify its use when the larger addend is 10 or above. These key questions develop number sense and strategic thinking, linking to subtraction as counting back and preparing for multi-digit work. Practice reinforces recognition of teens numbers and part-whole relationships.

Active learning benefits this topic through manipulatives like bead strings and number lines, where children physically enact the count. Games and partner talks make repetition engaging, helping children internalise the strategy faster than rote worksheets alone. Hands-on methods clarify when to count on versus other approaches, boosting confidence and retention.

Key Questions

1. Construct an addition problem that can be solved by counting on from 12.
2. Compare counting on with using number bonds to solve addition.
3. Justify when counting on is an efficient strategy for addition.

Learning Objectives

• Calculate the sum of two numbers up to 20 by counting on from the larger addend.
• Compare the efficiency of counting on versus using number bonds to solve addition problems.
• Justify when counting on is an appropriate strategy for solving addition problems within 20.
• Construct an addition word problem that can be solved using the counting on strategy.

Before You Start

Counting to 20

Why: Students need a secure understanding of the number sequence up to 20 to accurately count on.

Identifying the Larger Number

Why: The counting on strategy requires students to identify the larger of the two addends to begin their count.

Number Bonds to 10

Why: Familiarity with number bonds helps students understand part-whole relationships, which is foundational for comparing strategies.

Key Vocabulary

Counting on	A mental math strategy where you start from one number and count forward to find the total. For addition, you start with the larger number and count on the smaller number.
Addend	The numbers that are added together in an addition problem. For example, in 7 + 3 = 10, both 7 and 3 are addends.
Sum	The answer to an addition problem. In 7 + 3 = 10, 10 is the sum.
Number bonds	A visual representation showing the relationship between a whole number and its parts. For example, a number bond for 10 might show 7 and 3 as its parts.

Watch Out for These Misconceptions

Common Misconception

Always start counting from 1 or the first written number.

What to Teach Instead

Demonstrate with a number line: for 5 + 12, jump from 12 to 17. Pair discussions reveal why starting larger saves steps, building strategic choice through shared manipulatives.

Common Misconception

Counting on is the same as counting all objects from zero.

What to Teach Instead

Use two-colour counters: group the larger addend first, then count on the rest. Small group relays highlight the difference in speed, correcting via peer observation and teacher-guided talk.

Common Misconception

Counting on only works for adding 1 or 2.

What to Teach Instead

Practice with bead strings on problems up to +5. Whole-class chaining shows extension to larger addends, with active enactment helping children see and feel the pattern.

Active Learning Ideas

Pair Game: Counting On Snap

Prepare cards with addition facts to 20, larger addend first. Pairs take turns flipping cards and racing to count on aloud using fingers or counters. The first to say the sum correctly keeps the card; discuss any errors together before continuing.

20 min·Pairs

Small Groups: Number Line Hops

Provide mini number lines (0-20). Groups draw a problem card, identify the larger number, and take turns hopping forward while counting on. Record the sum and share one efficient aspect with the class.

30 min·Small Groups

Whole Class: Bead String Chain

Use class set of 20-bead strings. Teacher calls a problem; children slide beads from the larger addend and count on together. Pause for thumbs up/down checks, then reveal and justify the answer as a group.

25 min·Whole Class

Individual: Ten-Frame Builds

Children get ten-frames and counters. For each problem like 9 + 4, fill the frame to the larger number then add by counting on. Draw or write the sum and note if counting on was quick.

15 min·Individual

Real-World Connections

• A baker counting out cookies for an order might start with the 15 cookies already on the tray and count on 4 more to reach 19.
• A shopkeeper calculating the total cost of two items, one costing £12 and the other £3, can count on from 12 to find the total of £15.
• A child counting their building blocks might have 11 red blocks and add 5 blue blocks, counting on from 11 to find they have 16 blocks in total.

Assessment Ideas

Quick Check

Present students with a series of addition problems (e.g., 13 + 4, 9 + 6, 11 + 7). Ask them to solve each by counting on and record their answer. Observe their process and note any students struggling to start from the larger addend or maintain the count.

Discussion Prompt

Ask students: 'When is it easier to count on to solve an addition problem, and when might using number bonds be quicker? Give an example for each.' Listen for their reasoning about the size of the numbers involved.

Exit Ticket

Give each student a card with an addition problem, such as '14 + 3'. Ask them to write the answer and one sentence explaining how they found it using counting on. For example: 'I started at 14 and counted on 3 more: 15, 16, 17. The answer is 17.'

Frequently Asked Questions

What is adding by counting on in Year 1?

Counting on starts from the larger addend and counts forward by the smaller one, like 13 + 4: thirteen, fourteen, fifteen, sixteen, seventeen. It targets sums to 20 per KS1 standards, promoting mental fluency over counting all. Children practise through problems they construct, comparing to number bonds for deeper understanding.

How to construct addition problems solved by counting on from 12?

Use 12 as the larger addend with 1-8 more, such as 12 + 3 or 12 + 6. Ensure the second number is small for efficient counting. Children write their own, like 12 + 2 = ?, then solve and justify why counting on works well here versus smaller starts.

When is counting on an efficient strategy for addition?

It excels when the larger addend is 10 or more and the second is under 5, minimising counts. Compare to number bonds for 8 + 7, where bonds may be faster. Justification activities help children select strategies, aligning with Autumn Term goals.

How can active learning help teach counting on?

Games like number line relays and bead string chains let children physically count on, making the strategy concrete. Pairs racing to solve cards build speed and discussion skills, while whole-class demos correct errors instantly. These methods engage kinesthetic learners, improve retention over drills, and link to justifying efficiency through real-time peer feedback.