Growing by Subtracting

Overview

Lesson 3 of 8 in Growing Patterns, Powerful Rules. Students explore descending number patterns that decrease by a constant amount, moving from concrete collections to pictures, numbers and verbal rules. They identify missing terms and explain how they know.

Learning intentions

• WALT recognise a descending pattern that changes by the same amount each time.
• WALT represent a subtracting pattern using materials, pictures and numbers.
• WALT describe the rule for a pattern in words.
• WALT solve missing-term problems and explain our thinking.

Success criteria

• I can find the constant amount being subtracted.
• I can continue a descending pattern accurately.
• I can find a missing term and explain how I know.
• I can describe a pattern rule using words such as “subtract 5 each time”.

Curriculum links

• Number: use additive thinking to solve problems involving subtraction and differences.
• Algebra: recognise, continue and describe repeating or growing patterns using a rule.
• Mathematical practices: represent ideas in different ways, notice relationships, reason and explain.
• Communication and participation: listen to others’ strategies and use mathematical language to justify an answer.

Lesson structure (45 minutes)

1. 0–5 minutes – Notice the change

Open with the hook and pattern images. Show a collection of 18 counters, then remove 3; repeat until 9 remain. Ask: “What is changing? What stays the same?” Invite students to turn and talk, then share the phrase “subtract 3 each time”. Record both the concrete actions and the number pattern: 18, 15, 12, 9.

2. 5–12 minutes – Build and represent

In pairs, give students counters or linking cubes. Call out a starting amount within 20, such as 17, and a constant subtraction, such as 2. Students build the first collection, remove the same number each turn, and record the results. Use the concrete-to-picture examples to connect collections with drawings, numbers and the verbal rule.

Model the language: “The pattern starts at 17 and subtracts 2 each time.” Clarify that the pattern is descending because the numbers get smaller.

3. 12–20 minutes – Guided missing terms

Display patterns with one missing term, such as 20, 16, __, 8 and 19, __, 13, 10. Students solve on mini-whiteboards and show a matching drawing or subtraction equation. Ask: “What do you know already? How can you check your answer?” Discuss both counting backwards and using the constant difference.

4. 20–32 minutes – Partner practice

Distribute the descending patterns practice sheet. Partners complete the core questions: continue patterns, find missing terms and write the rule. Include the context problem: “A library has 40 books on a display. Each day, 5 books are removed. How many books are on the display after each day?” Students record the pattern and explain what the numbers mean.

Circulate and ask: “What is being subtracted?” “How do you know the missing number?” “Could you solve it from the other end?” Encourage complete explanations rather than answers only.

5. 32–38 minutes – Compare strategies

Select two or three student solutions to discuss. Include a strategy using repeated subtraction and one using the difference between known terms. Use the strategy discussion prompts to compare methods. Address the misconception that a descending pattern must subtract 1: the constant amount can be any suitable number.

6. 38–43 minutes – Create and challenge

Students create a descending pattern with at least five terms, then cover or remove the starting term and one other term. They swap with a partner, who identifies the missing information and explains more than one possible strategy. Students should check whether the available terms give enough information to determine the rule.

7. 43–45 minutes – Exit reflection

Display the plenary and exit questions. Students respond orally or on the bottom of the worksheet: “Complete 35, 30, __, 20. What is the rule? How do you know?” Invite one or two students to share a precise explanation.

Resources

• the complete lesson slide deck
• the descending patterns practice sheet
• Counters, linking cubes or small classroom objects
• Mini-whiteboards, pens and erasers
• Pencils and colouring pencils
• Prepared examples on the board
• One set of counters per pair

Assessment

• Observe whether students maintain the same subtraction amount when building and recording patterns.
• Check worksheet explanations, especially identification of the constant difference and interpretation of the library context.
• Use the final pattern response to identify students who can continue a pattern but cannot yet explain its rule.

Differentiation

• Support: work with concrete materials and subtraction stories within 20. Begin with patterns subtracting 1, 2 or 5, use a number line, and provide the sentence frame: “The rule is subtract ___ each time.”
• Support: reduce the number of terms and provide the starting number and constant subtraction. Pair students strategically and rehearse explanations orally before writing.
• Consolidate: use patterns such as 40, 35, 30, 25 and include missing terms in different positions.
• Extend: ask students to create a descending pattern where the starting information is missing. They must explain multiple strategies and discuss whether more than one starting number or rule could fit.
• EAL/SEN: use gestures for “remove” and “subtract”, colour-code each subtraction jump, provide visual examples and accept drawings, equations or oral explanations alongside written language.