What Is the Problem?

Overview

This is lesson 1 of 5 in the Model, Share and Solve unit. Students explore everyday situations involving adding, taking away, sharing equally and making groups. They use counters, blocks and drawings to identify what is known, what needs to be found and how the situation can be represented.

Learning intentions

Students will:

• identify the quantities and action in a simple mathematical situation
• decide whether a situation involves addition, subtraction, sharing or grouping
• model a situation using counters, blocks or a drawing
• explain what the problem is asking them to find
• listen to and compare different representations

Success criteria

• I can tell what numbers and objects are in a problem.
• I can explain what needs to be found.
• I can make a model or drawing to show the situation.
• I can explain whether I am adding, taking away, sharing or grouping.

Curriculum links

• Recognising, representing and solving practical addition and subtraction problems involving small whole numbers.
• Representing and solving simple equal-sharing and grouping situations using concrete materials and drawings.
• Using mathematical language to describe quantities, actions and solutions.
• Applying problem-solving strategies, reasoning, communication and representation.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook: What is the problem? Open with the hook and lesson introduction slides. Show a picture of 8 apples and ask: “What could be happening here? What might someone need to find out?” Accept different possibilities, such as adding more apples, taking some away or sharing them. Explain that mathematicians first work out what a problem is asking before solving it.

2. 5–12 minutes – Notice the quantities and action Use the problem story slides to present four short stories, one at a time:

• “There are 5 birds. 3 more arrive.”
• “There are 9 blocks. 4 are put away.”
• “12 counters are shared equally between 3 children.”
• “10 buttons are put into groups of 2.” For each, ask: “What do we know? What is happening? What do we need to find?” Record student language such as more, left, equal shares, groups of and altogether. Do not require students to calculate yet.

3. 12–17 minutes – Teacher modelling Model the first two stories with counters, thinking aloud: “I know there are 5 birds and 3 more arrive. I need to find how many there are altogether.” Draw a simple picture and write a matching number sentence. Briefly model sharing and grouping with counters, emphasising that sharing asks “How many in each group?” while grouping asks “How many groups can I make?”

4. 17–30 minutes – Partner investigation Place students in 10 mixed-ability pairs. Give each pair counters or blocks and the Twenty-frame Mats for building and organising quantities. Distribute the problem modelling worksheet. Read one problem from the worksheet at a time, or display it using the partner investigation instruction slides. Pairs build or draw what is happening, circle the quantities they know and complete the prompt: “We need to find ___.” Encourage partners to take turns as the builder and explainer.

5. 30–37 minutes – Sort and discuss strategies Invite pairs to place one completed model where classmates can see it. Guide students to sort examples under four headings: adding, taking away, sharing equally and making groups. Ask: “What clues helped you decide?” and “Could this problem be modelled another way?” Address the misconception that every problem can be solved by simply adding the visible numbers.

6. 37–42 minutes – Independent check Students complete the final problem on the problem modelling worksheet independently. They draw or use counters to show the situation and finish the sentence, “The problem is asking me to find…”. Circulate and ask students to explain their model rather than focusing only on a numerical answer.

7. 42–45 minutes – Plenary Return to the reflection and plenary slides. Ask students to complete the sentence orally: “Before I solve a problem, I should…” Invite two or three students to share a model. Reinforce the routine: notice the quantities, identify the action, represent the situation and say what must be found.

Resources

• the complete introduction, modelling, activity and plenary slide deck
• the problem modelling worksheet
• the Twenty-frame Mats
• Counters, linking blocks or small classroom objects
• Pencils, crayons and whiteboards
• Four labelled signs: adding, taking away, sharing equally, making groups
• Board or display space
• Prepared pairs and mixed-ability seating

Assessment

• Listen for students identifying known quantities, the action and the unknown during partner talk.
• Observe whether students use counters, drawings or grouping to represent the situation accurately.
• Check the independent worksheet response, particularly the explanation of what needs to be found, not just the calculation.

Differentiation

• Support: use smaller quantities, provide counters already organised in a frame and rehearse the language stems: “I know…”, “Something happens…”, “I need to find…”.
• Support: read problems aloud, use picture cues and pair students strategically; allow oral explanations or teacher scribing where writing is a barrier.
• EAL/D: pre-teach and gesture more, left, each, share, group and altogether; provide sentence frames and partner rehearsal.
• Extension: ask students to create a different story for the same model, or explain how a sharing problem differs from a grouping problem.