Count Back to Zero

Overview

Students explore subtraction within 20 by modelling numbers on a number line and counting back one step at a time. They notice and explain that subtracting zero does not change the starting number, building on prior work with counting forwards, backwards and representing quantities.

Learning intentions

• WALT subtract numbers within 20 by counting back.
• WALT use a number line or objects to show subtraction.
• WALT explain what happens when we subtract zero.
• WALT record subtraction equations using numerals and symbols.

Success criteria

• I can start at the first number and count back the number being subtracted.
• I can show my thinking with a number line, fingers or counters.
• I can write a subtraction equation to match my model.
• I can explain that subtracting zero leaves the number unchanged.

Curriculum links

• Mathematics and Statistics — Number: developing additive thinking through subtraction within 20.
• Mathematics and Statistics — Number: representing, solving and explaining simple addition and subtraction situations.
• Mathsteasers: using carefully chosen mathematical challenges to deepen understanding and encourage higher-order thinking.
• Mathematical practices: communicating mathematical ideas, using representations and explaining reasoning.

Lesson structure (45 minutes)

1. 0–5 min · Hook and activate. Open with the counting-back hook showing 12 apples and the question, “If 3 apples roll away, how many are left?” Act out the story with 12 counters; students count the starting amount, remove three and share how they found the answer.

2. 5–13 min · Teacher modelling. Use the number-line modelling slides and draw a large number line from 0 to 20. Model 15 − 4: place a finger on 15, make four jumps backwards, and say each number aloud: “14, 13, 12, 11.” Record 15 − 4 = 11. Explicitly teach: start at the first number, count back the second number, and land on the answer. Students copy the jumps in the air and repeat the language with a partner.

3. 13–21 min · Guided practice. Display examples from the guided practice slides such as 9 − 2, 17 − 5 and 20 − 3. Solve the first together using a floor number line or a drawn number line. For each remaining example, students show the jumps with their fingers or counters, tell a partner the answer and explain where they started and stopped. Check answers by counting the objects remaining.

4. 21–33 min · Partner activity. In pairs, students use the Numbers Flashcards to choose a starting number from 0–20, then choose a second number that is no greater than the starting number. They place counters on a number line, count back and say the matching equation. Include at least one turn with “subtract zero”. Partners take turns as the mathematician and checker: the checker asks, “Where did you start? How many did you count back? Where did you land?” Circulate, prompting students to touch or move one counter for each backward count.

5. 33–41 min · Independent practice. Revisit the independent practice instructions and distribute the counting-back subtraction worksheet. Students complete subtraction equations within 20 by drawing jumps, circling the starting number and writing the answer. The final questions include examples such as 8 − 0, 14 − 0 and 20 − 0. Ask students to complete the sentence, “When I subtract zero, the answer is ___ because ___.” Support students to use counters or a number line rather than relying on memory.

6. 41–45 min · Wrap-up. Show the plenary question: “Is 13 − 0 equal to 13? How do you know?” Students use a quick think-pair-share, then two or three explain using a representation. Finish with the class response: “Subtracting zero does not change the amount.” Collect the worksheet and note students who can explain this rather than only state the answer.

Resources

• the complete counting-back slide deck
• the counting-back subtraction worksheet
• the Numbers Flashcards
• Large floor number line from 0 to 20
• Individual number lines from 0 to 20
• Counters or small classroom objects
• Pencils and crayons
• Whiteboard and marker

Assessment

• During modelling, check whether students begin at the first number and make the correct number of backward jumps.
• During partner work, listen for accurate mathematical language, including “start at”, “count back” and “land on”.
• Review the worksheet, especially the zero questions and explanation sentence, to identify students needing further concrete practice.

Differentiation

• Support: provide a number line, counters and a reduced range such as numbers to 10; encourage students to touch one object or make one jump for each count-back number.
• Support language development with the sentence frame: “I started at ___. I counted back ___. I landed on ___.”
• For students who confuse the starting number and the number being subtracted, colour-code the first number as “start” and the second number as “jumps back”.
• Extend confident students by asking them to create a subtraction story for an equation and explain why 16 − 0 and 16 have the same answer.
• Pair students thoughtfully and accept oral explanations, pointing, movement or drawings as evidence of understanding.