Patterns and Strategies for 4s

Overview

Lesson 3 of 8 in the unit Multiplication and Division Facts. Students use arrays, equal groups and known multiplication facts to develop fluency with the 4-times facts, focusing on the double-double strategy.

Learning intentions

• Students will represent 4-times facts using equal groups and arrays.
• Students will use doubling and known facts to solve multiplication facts for 4.
• Students will connect 4-times facts to multiples of 4 and related facts.
• Students will explain and justify their strategy using mathematical language.

Success criteria

• I can represent a 4-times fact with equal groups or an array.
• I can use double-double or a near fact to solve a 4-times fact.
• I can recall and apply 4-times facts to 10.
• I can explain why doubling twice gives the same answer as multiplying by 4.

Curriculum links

• Multiplication and division: develop recall and proficiency with multiplication facts, including facts for 4.
• Number relationships: use arrays, equal groups, factors, products and related facts to represent multiplication.
• Mathematical reasoning: explain strategies, identify errors and justify solutions.
• Fluency and problem-solving: choose efficient mental and concrete strategies and communicate mathematical thinking.

Lesson structure (50 minutes)

1. 0–5 minutes – Warm-up and hook

Open with the opening question and array hook: “How could you solve 4 × 8 without counting in ones?” Display an array or build four groups of eight with counters. Invite students to share quick ideas, then introduce the vocabulary: quadruple, double, multiple, factor, product and related fact.

2. 5–17 minutes – Explicit teaching: double-double

Use the double-double teaching slides to model 4 × 6. First show two groups of six: 2 × 6 = 12. Double 12 to make four groups of six: 24. Say: “Multiplying by 4 is doubling, then doubling again.” Build the same fact with square tiles as a 4-by-6 array and partition it into two equal 2-by-6 halves.

Compare 4 × 5 = 20 and 4 × 10 = 40. Build a class 4s pattern by skip-counting: 4, 8, 12, 16, 20 … 40. Emphasise that 4 × 6 means four groups of six, not 6 + 4. Briefly discuss array orientation: turning an array shows the related fact, but the number of rows and items in each row must be identified accurately.

3. 17–25 minutes – Guided pair construction

In pairs, students use counters or square tiles to construct 4-times arrays for selected facts, such as 4 × 3, 4 × 7 and 4 × 9. Distribute the 4s arrays and strategy worksheet and ask students to draw each array, partition it into two equal halves and record the double-double steps.

Circulate and prompt: “What is the first double?” “What fact do you know?” and “How does your array prove your answer?” Students explain one array to their partner using a sentence stem: “I know ___ × ___ because I doubled ___ and then doubled ___.”

4. 25–32 minutes – Teacher-led missing facts

Use the guided practice and discussion slides for examples such as 4 × □ = 24, □ × 4 = 32 and 4 × 8 = □. Students solve on mini-whiteboards, show their answers together and explain their strategy.

Include a deliberate error: “4 × 7 = 11 because 7 + 4 = 11.” Ask students to identify and correct the error using an array or double-double reasoning. Reinforce that multiplication describes equal groups and that the product is the total.

5. 32–42 minutes – Independent fact sort and practice

Students complete a fact-sort task using their worksheet: place facts into known, developing and practise. They then answer individual 4s facts to 10 and complete short reasoning prompts, including “Show two ways to solve 4 × 8” and “Why does doubling twice give the same answer as multiplying by 4?”

Students who finish may use the multiplication facts strategy mat to choose another strategy, such as repeated addition, skip-counting or using a related 2s fact. Remind students that the aim is an efficient strategy, not simply a quick guess.

6. 42–47 minutes – Formative assessment checks

Conduct rapid mini-whiteboard checks: represent 4 × 4 as an array, solve 4 × 9 using double-double, complete 4 × □ = 36 and identify the product in 4 × 7. Use an observation checklist to note whether students represent equal groups accurately, apply both doubles and explain their reasoning.

Provide a brief guided-teacher group for students who are still doubling only once, confusing 4 × n with n + 4, or misreading array orientation. Use two-colour counters and a half-array template to make the two doubling steps visible.

7. 47–50 minutes – Exit ticket and review

Distribute the multiplication facts exit ticket slips. Students solve 4 × 8 in two ways and complete the reflection: “My most useful strategy was … because …” Invite two students to share different methods. Collect slips to plan the next lesson’s revision and grouping.

Resources

• the complete 4s multiplication slide deck
• the 4s arrays and strategy worksheet
• Counters in two colours
• Square tiles
• Grid paper
• Mini-whiteboards and markers
• Multiplication charts
• Prepared fact cards for the known/developing/practise sort
• Observation checklist
• the multiplication facts strategy mat
• the multiplication facts exit ticket slips

Assessment

• Observe pair work and use questioning to assess arrays, equal groups, double-double reasoning and correct vocabulary.
• Check mini-whiteboard responses for misconceptions, especially one doubling step and addition-based errors.
• Analyse the exit ticket for accuracy and whether students can solve 4 × 8 in two ways and explain why the strategies work.

Differentiation

• Support students with two-colour counters, half-array templates, multiplication charts, fact cards and a guided teacher group.
• Use sentence stems and partner rehearsal to support EAL learners and students who need help explaining reasoning.
• Reduce the number of facts for students requiring additional processing time, while maintaining concrete array representation.
• Extend confident students by deriving 4s facts from 2s facts, solving missing-factor problems and identifying errors in worked solutions.