Mathematics · Year 3 · Additive Thinking and Mental Strategies · Term 2

Multiplication Facts (7, 9)

Developing strategies for the more challenging multiplication facts of 7 and 9, including finger tricks.

• ACARA Content Descriptions
• AC9M3N05

About This Topic

Multiplication facts for 7 and 9 times tables develop efficient recall and mental strategies, aligning with AC9M3N05 in the Australian Curriculum. Students explore the finger trick for 9s: hold up ten fingers, fold down the finger matching the multiplier, and read the tens from the left and ones from the right, such as 9x3 yielding 27. They also examine patterns like the digits of 9 times products summing to 9 (9x4=36, 3+6=9) and strategies for 7s, including doubling 3.5 times or linking to known facts like 7x8 as half of 14x8.

This topic supports the additive thinking unit by connecting repeated addition to multiplication fluency. Students design mnemonics for tricky facts, analyze emerging patterns, and justify why 7 and 9 prove harder: irregular patterns lack the repetition of 2s, 5s, or 10s, demanding deeper strategies over rote learning.

Active learning benefits this topic because students create and test personal tricks in collaborative settings, making facts memorable through ownership. Pair shares and group games build confidence, as peers reinforce strategies during low-stakes practice, leading to stronger retention and flexible thinking.

Key Questions

1. Design a mnemonic or trick to help remember the 9 times table.
2. Analyze the patterns that emerge when multiplying by 9.
3. Justify why some multiplication facts are considered more difficult to learn than others.

Learning Objectives

• Design a mnemonic device or finger trick to accurately recall multiplication facts for 7 and 9.
• Analyze patterns within the 7 and 9 times tables to predict unknown facts.
• Explain the strategies used to solve multiplication facts for 7 and 9, such as doubling or relating to known facts.
• Justify why certain multiplication facts, like those involving 7 and 9, are more challenging to memorize than others.
• Calculate multiplication facts for 7 and 9 with increased fluency.

Before You Start

Multiplication Facts (2, 5, 10)

Why: Students need a solid foundation with simpler multiplication facts to build upon and compare strategies for more complex ones.

Repeated Addition

Why: Understanding multiplication as repeated addition is foundational for developing mental strategies for all multiplication facts.

Key Vocabulary

multiplication fact	A basic arithmetic fact that represents the product of two single-digit numbers, such as 7 x 8.
mnemonic device	A memory aid, such as a rhyme, pattern, or trick, used to help recall information, like the 9 times table finger trick.
pattern	A predictable sequence or arrangement of numbers, like the sum of digits in multiples of 9 always equaling 9.
strategy	A specific method or approach used to solve a problem, such as using known facts or doubling to find unknown multiplication facts.

Watch Out for These Misconceptions

Common Misconception

There are no patterns in the 7 times table.

What to Teach Instead

7 times products follow strategies like 7x6 as double 7x3 or links to 10x minus 3x. Small group chart-making reveals these connections visually. Peer discussions help students compare invented patterns, correcting the idea that 7s rely only on rote memory.

Common Misconception

Multiplying by 9 always ends in 9.

What to Teach Instead

9 times facts end in varied digits but sum to 9, like 9x7=63 (6+3=9). Finger tricks and pattern hunts in pairs make this tangible. Active sharing of examples builds consensus on the full pattern, reducing overgeneralization.

Common Misconception

All multiplication facts are equally easy to learn.

What to Teach Instead

Facts like 7x9 challenge due to fewer base-10 anchors than 5x or 10x. Justifying difficulties through class debates fosters reasoning. Collaborative strategy invention shows how tricks ease harder facts, promoting flexible approaches.

Active Learning Ideas

Finger Trick Practice: 9 Times Mastery

Demonstrate the finger method for 9x1 to 9x10. In pairs, students practice each fact, record products on mini-charts, and quiz each other. Pairs then teach one fact to the class using their chart.

20 min·Pairs

Pattern Discovery: Charting 7s and 9s

Provide grid paper for small groups to multiply 7 and 9 by 1-12 and highlight patterns, such as digit sums for 9s or links to 10s for 7s. Groups discuss findings and create posters. Share one pattern per group with the class.

30 min·Small Groups

Mnemonic Relay: Inventing Tricks

In small groups, assign hard facts like 7x8 or 9x7. Groups design rhymes, drawings, or stories as mnemonics. Relay-style, one member performs the mnemonic while others guess the fact, then rotate roles.

25 min·Small Groups

Fact Fluency Bingo: 7s and 9s

Distribute bingo cards with products from 7 and 9 tables. Call facts randomly; students mark matching products. First to complete a row shouts the fact chain used, reviewing strategies aloud.

15 min·Whole Class

Real-World Connections

• Bakers often need to quickly calculate quantities for recipes, for example, if a recipe calls for 7 cookies per batch and they need to make 9 batches, they must calculate 7 x 9 = 63 cookies.
• Event planners might need to determine seating arrangements for a conference. If they have 9 tables and need to seat 7 guests at each, they would use multiplication to find the total number of seats needed: 9 x 7 = 63 seats.

Assessment Ideas

Quick Check

Present students with a list of 7 and 9 times table facts, including some they haven't explicitly practiced. Ask them to write down the answer and the strategy they used to find it (e.g., 'used finger trick', 'doubled 3.5', 'related to 7x7').

Exit Ticket

Give each student a card with a multiplication fact for 7 or 9. Ask them to write the answer and draw a picture or write a sentence explaining a trick or pattern that helps them remember that specific fact.

Discussion Prompt

Pose the question: 'Why do you think the 7 and 9 times tables are harder for some people to learn than the 2 or 10 times tables?' Facilitate a class discussion where students share their reasoning, referencing patterns and strategies.

Frequently Asked Questions

How do you teach the finger trick for 9 times table in Year 3?

Start with hands up representing 10 fingers. For 9x5, fold the fifth finger: four fingers left mean 40, five right mean 5, so 45. Pairs practice all facts, drawing hands on paper for reference. This visual kinesthetic method builds instant recall, with class demos reinforcing correct form for consistent results.

What patterns help Year 3 students remember 7 and 9 multiplication facts?

For 9s, digits sum to 9 (e.g., 9x6=54, 5+4=9); for 7s, use 10x minus 3x (7x4=28, as 40-12). Groups chart facts to spot these, then create visuals. This analysis turns memorization into discovery, strengthening connections across facts for long-term fluency.

Why are 7 and 9 times tables harder for Year 3 students?

These facts lack simple patterns like even numbers in 2s or zeros in 10s, requiring strategies over pure repetition. Students justify this by comparing table charts. Building tricks collaboratively addresses the gap, as peers model flexible thinking that rote practice alone misses.

How does active learning improve multiplication facts recall in Year 3?

Active methods like pair quizzing, group mnemonic creation, and bingo games engage multiple senses, boosting retention over worksheets. Students own strategies through invention and sharing, gaining confidence in mental math. Collaborative pressure simulates real use, while immediate feedback corrects errors, leading to fluent recall aligned with AC9M3N05.