Finding factors with T-charts: a practical lesson plan
A T-chart gives students a clear visual way to find factor pairs and understand how numbers are built through multiplication. Instead of guessing isolated answers, learners record one factor on the left, its matching factor on the right, and gradually see a complete list develop.
This lesson is suited to upper-primary students who are learning multiplication facts, divisibility, and number relationships. It can be used in an Australian classroom, at home, or during tutoring sessions in Brisbane, Melbourne, Perth, Sydney, or smaller regional communities. The activities work well as a printable maths lesson with guided examples, independent practice, and a short exit check.
Learning goals and preparation
By the end of the lesson, students should be able to explain what a factor is, find factor pairs for a given whole number, and use a T-chart to organise their thinking. They should also recognise that factor pairs multiply to make the target number and identify special cases such as square numbers, which have a repeated factor.
Prepare a set of blank T-chart worksheets, pencils, mini-whiteboards, and a collection of number cards. Choose accessible numbers such as 12, 18, 20, 24, and 30 before moving to larger values such as 48, sixty, or 72. For Australian classrooms, a black-and-white printable version is useful when teachers need economical photocopying for a full class, while a digital version suits students working on tablets at home.
Write the target number at the top of each chart. Label one column “Factor” and the other “Matching factor”. Students can then record pairs in order, beginning with 1 and checking each possible divisor.
Introducing factors through arrays
Begin with a familiar multiplication fact. Display 24 and ask students to build it with counters, grid paper, or drawn rows. Six rows of four counters show that 6 and 4 are factors of 24. Turning the array or describing it as four rows of six demonstrates why factor pairs can be written in either order.
Explain that a factor divides a number exactly, with no remainder. Model a T-chart for 24:
| Factor | Matching factor |
|---|---|
| 1 | 24 |
| 2 | 12 |
| 3 | 8 |
| 4 | 6 |
Discuss how the pairs are connected: 1 × 24, 2 × 12, 3 × 8, and 4 × 6. Once the next trial factor would repeat a pair, the list is complete. This helps students avoid writing the same relationship twice.
Connect the activity to multiplication fluency without making speed the main goal. Students who need extra support can use a times-table chart or counters, while confident learners can explain why a number such as 25 has fewer factor pairs than 24.
Modelling a systematic method
Show students how to test possible factors in a sensible order. Start with 1, then 2, 3, 4, and so on, asking whether each number divides the target exactly. For a target of 36, students can identify 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. Point out that the central pair repeats the same factor because 36 is a square number.
Use verbal prompts such as “What multiplication fact makes this number?” and “How can we prove that no pair is missing?” These prompts encourage reasoning rather than random trial and error. Students may use skip-counting, known times tables, repeated addition, or written division to verify each pair.
Once learners are comfortable with the chart, connect factor knowledge to later calculation work. A student who recognises 24 as 3 × 8 can use that relationship when breaking apart a larger multiplication problem. For a related review of written strategies, teachers can use double-digit multiplication strategies alongside factor-pair practice.
Guided and independent practice
Work through two examples as a class, gradually reducing the amount of teacher assistance. Suitable guided numbers include 16 and 40 because they offer several pairs without overwhelming students. Invite learners to justify each entry and ask classmates to check whether the products are correct.
For independent work, provide a mixture of targets: prime numbers such as 13, composite numbers such as 28, and square numbers such as 49. Students can complete a T-chart, list the multiplication equations underneath, and circle the pair with the closest values. This final step helps them notice that factor pairs move towards the square root of the target.
A classroom activity can turn the worksheet into a matching game. Give pairs of students cards containing numbers and separate cards containing factor pairs. They match the cards, then verify each relationship with a T-chart. In an Australian school setting, this works well as a short numeracy rotation before recess or as a focused activity during a maths group.
Differentiation and assessment
Students who are still developing multiplication recall can work with numbers below 30, use arrays, or receive a partially completed chart. Colour-coding the two members of each pair can make the relationship easier to see. A teacher, parent, or tutor can also provide a multiplication grid and encourage students to explain their choices aloud.
Extend advanced learners by asking them to find all factors of 72, compare the factor lists of 36 and 48, or create a number with exactly six factors. They might investigate which numbers from 1 to 50 are prime, or explain why every even number greater than 2 is composite. These challenges suit extension groups and homeschool lessons where students can explore patterns at their own pace.
Assess understanding through observation, completed charts, and a brief exit ticket. Ask students to list the factor pairs of 30, identify whether 31 is prime or composite, and explain how they know. Look for accurate multiplication, complete pairings, and clear reasoning rather than neatness alone.
T-charts turn factor finding into an organised, visual routine that students can reuse across many number topics. Download printable factor worksheets from Gialdini Worksheets and use them for classroom practice, home learning, tutoring sessions, or revision during the Australian school holidays. Select a target number, model one chart, and give learners regular opportunities to explain the multiplication relationships they discover.