Divisibility Pattern Review

Overview

In this second lesson of the Linear Patterns and Algebra unit, students rebuild essential number sense by identifying and explaining divisibility rules for 2, 5, and 10. Concrete sorting, place-value modelling, oral rehearsal, and independent practice prepare students to notice and describe numerical patterns in later algebra work.

Learning intentions

Students will:

• explain what it means for a number to be divisible by 2, 5, or 10;
• use place-value patterns and number endings to classify numbers;
• justify why a number is or is not divisible;
• communicate mathematical thinking orally, pictorially, and symbolically.

Success criteria

• I can state the divisibility rule for 2, 5, and 10.
• I can sort numbers according to whether they are divisible by each rule.
• I can explain my choice using the number’s ones digit.
• I can check my answer by using counters, a known fact, or division.

Curriculum links

• Number — determine and explain why numbers are divisible by 2, 5, and 10.
• Patterns and Relations — recognize and describe oral and written patterns and their corresponding relations.
• Mathematical processes — communication, connections, mental mathematics and estimation, problem solving, reasoning, and visualization.
• Report card evidence — Knowledge and Understanding, Mental Math, and Problem Solving.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Teacher displays three large numbers—24, 35, and 70—and asks, “What do these numbers have in common?” Students make a private prediction, then share one observation with a partner before the teacher records all reasonable ideas. Open the hook and learning-intention slides to establish the focus and connect to prior work with factors and patterns.

2. 5–13 min · Explicit instruction. Teacher uses place-value cards and counters to model equal groups of 2, 5, and 10, then co-constructs a visual chart: divisible by 2 means the ones digit is 0, 2, 4, 6, or 8; divisible by 5 means the ones digit is 0 or 5; divisible by 10 means the ones digit is 0. Students build and test examples such as 18, 25, 40, and 73, recording the rule in the guided divisibility notes and practice sheet. Use the rule chart and place-value modelling slides to keep the examples visible.

3. 13–23 min · Video and guided reasoning. Teacher shows a short, age-appropriate divisibility video about 2, 5, and 10, pausing after each rule to ask, “What did you notice about the ones digit?” Students complete one guided-note box after each pause and orally rehearse the sentence frame: “___ is/is not divisible by ___ because its ones digit is ___.” Return to the video discussion and sentence-frame slides for the prompts and visual summary.

4. 23–34 min · Mathology sorting investigation. Teacher provides the Mathology divisibility sorting activity and supports students in sorting number cards into “divisible by 2,” “divisible by 5,” “divisible by 10,” and “not divisible by any.” Students work as a group of four, taking turns as reader, sorter, checker, and explainer; they may use counters or place-value cards to verify uncertain choices. After each sort, one student explains the rule used while classmates agree, revise, or ask a question.

5. 34–42 min · Supported digital and written practice. Teacher assigns a short, targeted Mathletics practice set, first completing one item together and highlighting the ones digit. Students then complete selected questions on the independent classification and explanation section, including mixed examples and one “convince me” question. Teacher conferences briefly with each student, prompting “Which digit matters?” rather than giving the answer.

6. 42–48 min · Evidence checkpoint. Teacher gives each student six numbers: 14, 27, 30, 45, 62, and 91. Students sort them, state the rule used for each relevant choice, and explain one choice orally or in writing. Students may refer to the visual rule chart and checkpoint instructions but must make the classification independently.

7. 48–50 min · Exit reflection. Teacher asks students to complete the final prompt on the exit reflection box: “A number is divisible by 10 if…,” followed by one example and a confidence rating. Students share one strategy they will use next time; teacher previews that these patterns will support algebraic rules.

Resources

• the divisibility review slide deck
• the guided notes and independent practice worksheet
• Teacher-selected short divisibility video about 2, 5, and 10
• Mathology divisibility sorting activity and number cards
• Place-value cards
• Two-colour counters or connecting cubes
• Mini-whiteboards and markers
• Devices and headphones for Mathletics practice
• Pencils, highlighters, and visual rule chart

Assessment

• Knowledge and Understanding: Listen for accurate statements of the three rules and review the guided notes, sorting task, and independent classifications. Progress is shown when a student correctly identifies divisibility using the ones digit and makes no more than one rule error.
• Mental Math: During the hook, modelling, and checkpoint, record whether each student quickly identifies relevant endings without calculating the full quotient. Progress is shown when the student uses the rule efficiently for at least four of six numbers.
• Problem Solving: Use the six-number checkpoint to document whether students classify, select an appropriate rule, and justify one decision orally or in writing. Progress is shown when the student provides a correct classification and a mathematically valid explanation.
• Record evidence under the Manitoba report card descriptors for Knowledge and Understanding, Mental Math, and Problem Solving; note whether performance is independent, supported, or not yet demonstrated.

Differentiation

• Provide colour-coded rule cards, highlighted ones digits, enlarged print, accessible spacing, and a worked example; allow students to keep the visual chart beside the worksheet.
• Use counters and place-value cards before symbolic work. Reduce the checkpoint to three numbers for students on modified programs, while retaining the expectation to explain one choice.
• Offer oral rehearsal, sentence starters, partner reading, audio directions, and dyslexia-friendly text: clear sans-serif font, generous spacing, short lines, minimal visual clutter, and no unnecessary copying.
• Maintain four predictable group roles and use brief, timed turns to support distractible students. For students ready for challenge, ask them to create a number divisible by both 2 and 5 and explain why that also makes it divisible by 10.