Count On and Back

Overview

This is lesson 4 of 5 in Tatau, Tāpiri, Tango. Students use a number line to solve addition and subtraction problems within 20, choosing whether to count forwards or backwards and explaining their thinking in English and te reo Māori.

Learning intentions

• WALT use a number line to add and subtract.
• WALT count on and count back from a given number.
• WALT explain how my jumps show my calculation.
• WALT notice when a strategy is efficient.

Success criteria

• I can start at the correct number.
• I can move the correct number of spaces.
• I can explain where I landed.
• I can say or show whether I counted on or counted back.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: relevant challenge connected with classroom mathematics learning.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners, including opportunities to compare and justify strategies.

Lesson structure (30 minutes)

1. 0–5 min · Warm-up: tatau and jump. Display the bilingual number-line warm-up and lead the class in counting from 0 to 20 and back, using the words tatau (count), whakamua (forwards), whakamuri (backwards), tāpiri (add) and tango (subtract). Students take turns making small jumps on a large floor number line while the class says the numbers in English and te reo Māori.

2. 5–13 min · Model: count on and count back. Use the teacher modelling slides and a large number line. Model 7 + 5 by starting at 7 and making five forward jumps: “I count on because I am adding.” Then model 14 − 6 by starting at 14 and making six backward jumps. Include 8 + 5 and 13 − 6 to show crossing through 10. Students echo the language, point to the starting number, and show the direction of movement with their hands.

3. 13–18 min · Partner activity: mystery number jumps. Display the mystery-jump instructions. One partner secretly chooses a start number and gives a number of forward or backward jumps; the other partner works out the landing number and explains the calculation. Partners swap roles after each turn. Prompt: “Where did you start? Which way did you move? How many spaces? Where did you land?”

4. 18–27 min · Small-group practice. Organise three teacher-chosen groups of approximately 6–7 students and provide the number-line practice sheet for recording or pointing to answers. Rotate briefly between groups, checking that each student begins at the correct number.

• Emerging: Use a floor number line and physical jumps. Give addition and subtraction facts within 10 first, then include one problem crossing through 10.
• Developing: Use bead strings or open number lines to solve mixed facts within 20. Encourage students to bridge to 10, such as 8 + 5: “2 to 10, then 3 more.”
• Consolidating: Students select the most efficient strategy for mixed facts to 20 and explain their choice to a partner. Include problems such as 9 + 6, 15 − 7, 7 + 8 and 16 − 9.

5. 27–30 min · Exit check and share. Return to the exit-check slide. Give each student one problem, such as 8 + 6 or 15 − 7. Students solve by drawing, moving, pointing or explaining orally, then show the starting number, direction, number of jumps and landing number. Invite one student to share a clear explanation.

Resources

• the bilingual number-line lesson deck
• the number-line practice sheet
• Large floor number line labelled 0–20
• Chalk, masking tape or floor markers
• Bead strings or two-colour counting strings
• Counters or small Māori-inspired natural materials, such as stones or shells
• Mini whiteboards and pens
• Group labels: Emerging, Developing, Consolidating

Assessment

• Observe during modelling and group work: Can students start at the correct number, move in the correct direction and make the correct number of jumps?
• Listen for explanations using “count on”, “count back”, “tāpiri”, “tango”, “whakamua” and “whakamuri”.
• Use the exit check to identify students needing further work with direction, starting numbers or crossing through 10. Record whether each student solved independently, with equipment or with prompting.

Differentiation

• Support: Keep the floor number line visible and use arrows, large numerals and colour coding: green for the starting number, blue for counting on and red for counting back. Give one instruction at a time and use verbal prompts such as, “Point to the start. Which way? Now move one space.”
• Dyslexia-friendly options: Use uncluttered, large-print resources, clear sans-serif numerals, strong contrast and plenty of white space. Permit students to point, move, speak, draw arrows or use counters instead of writing lengthy explanations.
• EAL and bilingual support: Pair actions with gestures and repeat sentence frames: “I started at __. I moved __ spaces __. I landed on __.” Accept explanations in te reo Māori, English or both, and invite whānau language knowledge where appropriate.
• Challenge and confidence: Allow students to choose equipment before moving to a mental strategy. Ask advanced learners to justify why counting on or counting back is more efficient for a particular problem.

Extension

• Solve the same problem in two ways, such as using a floor number line and a bead string, then compare which method was more efficient.
• Create a mystery-jump problem for another student and explain how the clues prove the starting and landing numbers.