Multiplying by 8 with Doubling Tricks and Patterns

Multiplying by 8 becomes easier when students see it as a familiar doubling process rather than a fact list to memorise. This lesson uses mental strategies, visual models and repeated patterns to help primary learners build confidence with the 8 times table.

The central idea is simple: double a number, double it again, then double it once more. For example, 6 × 8 can be solved as 6 × 2 = 12, 12 × 2 = 24, and 24 × 2 = 48. Students learn why the strategy works while developing recall of multiplication facts.

The activities suit Australian classrooms, home learning and tutoring sessions from the middle primary years. They can support work connected with the Australian Curriculum, especially lessons involving multiplication, mental computation, number patterns and efficient calculation strategies.

Prepare a whiteboard, pencils, counters, paper strips and a set of printable multiplication worksheets. A black-and-white version is useful for families and schools managing printing budgets during a busy school term in Sydney, Adelaide or regional Queensland.

Learning goals and preparation

By the end of the lesson, students should be able to use doubling three times to calculate a number multiplied by 8, identify patterns in the 8 times table and explain their mental strategy. They should also connect multiplication equations with equal groups, arrays and repeated addition.

Write several examples on the board, such as 3 × 8, 5 × 8, 7 × 8 and 9 × 8. Keep counters in groups of eight so students can check their thinking. For younger learners, use smaller numbers first; confident Year 4 students can move quickly to two-digit numbers such as 14 × 8 and 25 × 8.

Begin with a short warm-up on doubling. Ask students to double 2, 4, 6, 10 and 15, then double each answer again. This establishes the sequence needed for multiplying by 8 without introducing a new rule before the basic idea is secure.

Build the strategy through doubling

Model 7 × 8 as 7 × 2 × 2 × 2. Start with 7, double to 14, double to 28, and double to 56. Record the calculation vertically so students can follow each stage: 7 → 14 → 28 → 56. Explain that multiplying by 8 is equivalent to doubling three times because 8 is 2 × 2 × 2.

Invite students to solve 4 × 8, 10 × 8 and 12 × 8 with counters or drawings. A student might draw four groups of eight, while another uses 4 → 8 → 16 → 32. Accept both methods and discuss when a mental strategy is quicker than counting individual objects.

Connect the strategy to Australian money by using examples such as eight 20-cent coins or eight 50-cent coins. A pretend market stall with prices of $3, $5 and $7 can make the calculations meaningful, while reminding students that multiplication describes equal groups rather than repeated shopping.

Investigate patterns in the facts

Display the 8 times table from 0 × 8 to 12 × 8. Ask students to highlight the ones digits: 0, 8, 6, 4, 2, 0, 8, 6, 4, 2, 0, 8, 6. The repeating cycle helps learners check an answer, although it should be presented as a clue rather than a replacement for understanding.

Students can also examine the tens and ones digits in the sequence 8, 16, 24, 32, 40, 48, 56, 64, 72 and 80. Have them describe what changes from one fact to the next. Some will notice that each answer increases by 8, while others may recognise alternating even digits.

Create a missing-number puzzle with examples such as 8 × __ = 48, __ × 8 = 72 and 64 ÷ 8 = __. Include multiplication and division together so learners see the relationship between inverse operations. This is useful preparation for later work with fact families.

Practise with models and written calculations

Give each student a worksheet containing arrays, number lines and multiplication equations. For 6 × 8, learners can shade six rows of eight squares, label the array and write the doubling chain. Moving between a visual model and a symbolic equation helps students who find bare number facts difficult.

Use a gradual sequence: solve with counters, solve with a drawing, explain the doubling strategy aloud, then calculate mentally. Include a few two-digit examples such as 16 × 8. Students can double 16 to 32, then 64, then 128. Encourage them to estimate first so they can identify an unreasonable answer.

For a lively partner activity, use domino multiplication game ideas to generate random factors. One partner turns over a domino, chooses one side as the factor and multiplies it by 8; the other checks the result using three doublings or an array.

Differentiate for varied learners

Students needing support can work with facts from 1 × 8 to 5 × 8, use a times-table grid and keep a doubling card beside their worksheet. Colour-coding each stage—first double, second double, third double—makes the process easier to remember. A short session in a quiet corner may help learners who become overloaded by large tables.

Students ready for extension can calculate 18 × 8, 24 × 8 and 35 × 8 using partitioning. For example, 35 × 8 can be solved as 30 × 8 plus 5 × 8, giving 240 + 40 = 280. They can then write their own word problems using Australian contexts such as seats in cricket stands, packets at a school fete or produce boxes at a Brisbane market.

For learners who speak languages other than English, pair equations with diagrams and clear mathematical vocabulary: factor, product, equal groups and double. Avoid treating quick recall as the only evidence of progress. A student who explains a reliable strategy deserves recognition even when the answer takes longer.

Check understanding and extend the learning

Finish with a brief exit ticket containing four tasks: solve 8 × 6, show three doublings for 9 × 8, complete the pattern 16, 24, 32, __, __, and explain how to check 7 × 8. Review the responses to identify whether a learner needs help with doubling, place value or multiplication notation.

For an informal assessment, ask students to choose one fact and explain it to a partner without reading from the table. Listen for accurate language such as “I doubled 11 three times” and “11 groups of 8 is 88.” Record observations for future small-group planning during the next maths session.

Extend the lesson with division facts, fact-family triangles and short word problems. In a Perth classroom, a teacher might use eight equal teams collecting materials; at home, a parent might use eight packs of four stickers. These simple contexts give repeated practice without making the activity feel like rote drilling.

Print the lesson materials, select the support level that suits each learner and revisit the doubling chain across the week. Regular five-minute practice, paired explanations and pattern spotting can turn the 8 times table into a manageable, meaningful part of everyday numeracy.