Related Division Facts

Overview

Lesson 6 of 8 in the unit Multiplication and Division Facts. Students use known 3, 4, 5 and 10 multiplication facts to solve, represent and explain exact division problems through sharing, grouping and inverse operations.

Learning intentions

Students will:

• Connect division facts to known multiplication facts.
• Represent division by sharing equally and grouping.
• Solve exact division problems involving 3, 4, 5 and 10.
• Explain and check answers using multiplication.

Success criteria

• I can identify the multiplication fact that helps me.
• I can solve exact division problems.
• I can represent division using equal groups or sharing.
• I can check my answer with multiplication.

Curriculum links

• Apply known multiplication facts to related division facts.
• Represent and solve multiplication and division problems using materials, drawings and equations.
• Explain mathematical reasoning using appropriate language and inverse operations.
• Use mathematical proficiency: understanding, fluency, problem-solving and reasoning.

Lesson structure (50 minutes)

1. 0–5 minutes – Warm-up and hook

Display the question on the opening and warm-up slides: “If 24 objects are put into groups of 3, how many groups will there be?” Students think, discuss with a partner and share strategies. Revise the vocabulary dividend, divisor, quotient, equal groups, inverse.

2. 5–15 minutes – Explicit teaching

Use counters and the division sharing mats to model 24 ÷ 3. Make equal groups of 3, count 8 groups and record:

• 24 ÷ 3 = 8
• 3 × 8 = 24

Explain that the divisor tells the group size when grouping, while the quotient tells the number of groups. When sharing 24 between 3 people, the divisor tells the number of shares and the quotient tells how many are in each share. Model 40 ÷ 5 and 50 ÷ 10, emphasising the related multiplication facts. Refer to the worked-example slides and ask, “What multiplication fact helps us?”

3. 15–30 minutes – Guided practice

Place students in pairs. Give each pair counters, cups or hoops and the division sharing mats. Present stories one at a time, such as:

• 12 pencils shared equally between 3 students.
• 20 shells placed in groups of 5.
• 40 stickers shared equally between 4 children.
• 50 counters placed in groups of 10.
• 36 objects placed in groups of 4.

Pairs choose whether sharing or grouping is the clearest representation, build the model, write the division equation and record the multiplication check. Use the guided-practice prompt slides to display each story. Invite pairs to explain how the divisor and quotient are shown.

4. 30–40 minutes – Independent rotation tasks

Students rotate through three short tasks, approximately three minutes each, using the rotation-instruction slides:

• Match division facts with their answers using the division facts matching cards.
• Build and draw selected equations on a division mat.
• Complete the related division facts and multiplication checks on the independent practice worksheet.

Include facts based on 3, 4, 5 and 10 times tables. Circulate, checking that students make equal groups rather than simply count objects.

5. 40–46 minutes – Hinge questions

Display one question at a time on the hinge-question slides. Students answer on mini-whiteboards and hold them up:

• What multiplication fact helps solve 30 ÷ 5?
• In 40 ÷ 4 = 10, what does the 4 tell us?
• Which check proves that 36 ÷ 4 = 9?
• Is 25 ÷ 5 the same fact family as 25 ÷ 4? Explain.

Address errors immediately, particularly using the wrong divisor or confusing the number of groups with the number in each group.

6. 46–50 minutes – Exit ticket and reflection

Students complete the exit ticket section of the independent practice worksheet: solve 36 ÷ 4 and show the multiplication check. Respond to the reasoning question: “Can 30 ÷ 5 and 30 ÷ 6 belong to the same fact family? Why or why not?” Finish with the plenary slide and ask students to state one strategy they used.

Resources

• the complete lesson slide deck
• the independent practice worksheet
• the division facts matching cards
• the division sharing mats
• Counters, approximately 100
• Cups or hoops for making groups
• Mini-whiteboards and markers
• Pencils and erasers
• Timer

Assessment

• Observe pair work for equal grouping, correct use of the divisor and clear equation recording.
• Use mini-whiteboard responses to identify misconceptions and select students for follow-up.
• Collect the worksheet exit ticket to assess solving, representation, multiplication checking and reasoning.

Differentiation

• Support students with counters, sharing mats, visual bar models, smaller numbers and oral sentence frames: “I used ___ × ___ = ___, so ___ ÷ ___ = ___.”
• Work with a targeted group to rehearse 3, 4, 5 and 10 facts using concrete materials before recording equations.
• Provide EAL/D and students requiring adjustments with illustrated vocabulary, partner talk, repeated modelling and reduced task-card choices.
• Extend students with missing-dividend or missing-divisor problems, such as ___ ÷ 5 = 8 and 40 ÷ ___ = 8, and ask them to compare sharing and grouping interpretations.