Growing by Adding

Overview

Lesson 2 of 8 in Growing Patterns, Powerful Rules. Students investigate number patterns that increase by a constant whole-number amount, using number lines, bead strings and diagrams. They describe the rule using language such as “add 2 each time” and connect the pattern to a growing plant.

Learning intentions

• WALT recognise and continue patterns that grow by the same amount.
• WALT use number lines, bead strings and diagrams to show a pattern.
• WALT describe a pattern rule using “add ___ each time”.
• WALT solve a simple problem involving a constant weekly increase.

Success criteria

• I can find the amount added between terms.
• I can continue a growing pattern accurately.
• I can explain the rule in words and show it in a diagram or number line.
• I can work backwards from a later term to find an earlier term.

Curriculum links

• Number: use additive thinking to solve problems and explain strategies.
• Algebraic thinking: recognise, continue and describe simple growing patterns.
• Mathematical practices: represent, notice relationships, reason, communicate and justify.
• Te Mātaiaho capabilities: use mathematical language, make connections and explain thinking.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook: What is growing? Open with the pattern hook and learning intention slides. Display the sequence 5, 7, 9, 11 and ask: “What do you notice? What might come next? How do you know?” Students think independently, then share with a partner. Record different ways of describing the pattern.

2. 5–13 minutes – Model the constant increase Use a large number line and a bead string to model 5, 7, 9, 11. Emphasise that each term is found by adding 2, not by simply counting the numbers shown. Say and display: “The rule is add 2 each time.” Invite students to show the next two terms and explain how the jumps on the number line match the groups of beads.

3. 13–22 minutes – Partner investigation In pairs, students use counters, bead strings or drawn number lines to investigate patterns such as 2, 5, 8, 11 and 10, 14, 18, 22. Open the investigation instructions and pattern examples. For each pattern, students identify the increase, continue it by three terms and describe the rule to their partner. Circulate and ask, “How can you prove the amount added stays the same?”

4. 22–32 minutes – Plant-growth problem Display the plant problem from the plant-growth problem and discussion prompt: “A plant is 8 cm tall. It grows 3 cm each week. How tall will it be after four weeks?” Students represent the situation with a number line, repeated addition, bead groups or a diagram. Discuss whether the starting height is counted as week 0, and build the sequence 8, 11, 14, 17, 20. Stress that the rule is “add 3 each week.”

5. 32–40 minutes – Individual practice Distribute the growing-by-adding practice worksheet. Students complete pattern questions and explain at least two rules in words. The worksheet includes an enabling section with smaller numbers and number-line prompts, a core section requiring continuation and explanation, and an extension requiring students to work backwards from a later term.

6. 40–45 minutes – Share, justify and exit check Return to the plenary and exit-question slides. Invite two students to explain different representations of the same pattern. Students respond orally or on the back of the worksheet: “The pattern is 6, 10, 14, 18. What is the rule, and what comes before 6 if the pattern continues backwards?” Collect responses to identify students ready for the next lesson.

Resources

• the complete lesson slide deck
• the growing-by-adding practice worksheet
• Large classroom number line
• Bead strings or linking cubes
• Counters or small blocks
• Whiteboards and pens
• Pencils and erasers
• Chart paper or board space for recording rules

Assessment

• Listen for whether students identify the constant increase rather than just list the next number.
• Check representations and explanations during partner work and the plant-growth problem.
• Use the worksheet and exit response to group students for the next lesson: needing support, working securely, or ready to reason backwards and justify.

Differentiation

• Support: use smaller increases such as 1, 2 or 3; provide a marked number line, physical beads and the sentence frame “The rule is add ___ each time.”
• Consolidation: include patterns with different starting numbers and require students to continue and explain them using two representations.
• Extension: give a later term, such as “The fifth term is 23 and the pattern adds 4. What could the first term be?” Ask students to justify each step working backwards.
• EAL/SEN: pre-teach and display term, rule, increase, each time and backwards. Pair students strategically, read problems aloud and accept spoken, drawn or practical explanations before written recording.