Toolkits�Maths Talks for Thinking & Discussion�Day 1 - Tues 11th March�Time - 3.30 pm

Maths Talks for Thinking & Discussion

Boost student engagement, communication and mathematical thinking with fun, meaningful, and accessible Maths Image Talks. Encourage rich interactions that make students’ reasoning visible and deepen understanding through practical strategies that support the implementation of the NZC.

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Day 1 Tues 11th March

Time - 3.30 pm

Suitable for: anyone

Level: primary - kura tuatahi

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Elena Terekhina

Meet Link

elena.terekhina@manaiakalani.org

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Protocol in our online Meetings

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Test out your speaker and microphone in the settings prior to the meet

4 Components of a Comprehensive Maths Programme

Positive Relationships

Learning in maths is enhanced when students succeed in and feel positive about their learning.

Communication

Develop students’ knowledge, processes, and dispositions in mathematics and statistics.

Explicit Teaching

is an interactive, structured, carefully sequenced approach to teaching

(connect to prior knowledge, provide clear explanations with student input and discussion, model and demonstrate, check understanding, offer practice).

Rich Tasks

Meaningful problem-solving and investigation experiences designed to spark curiosity and engagement.

Mathematical Discourse

Communication: Plan for students to actively listen to, reflect, and build on each other’s thinking and learning. Use discourse-based tools and a range of open questions to facilitate productive discussions.

Maths Talks as ‘Enablers’ and Extenders’

• Encourage critical, creative and logical thinking;
• Promote communication, reasoning, and problem-solving skills;
• Develop conceptual understanding, number sense and mathematical fluency

Maths Talks

Ground Rules for Talk

• Actively listen (includes not talking over others)
• Respectfully take part giving ideas, reasons and evidence
• Ask questions
• Be inclusive. Invite the participation of others.
• Stick to the topic
• Look at other learners’ solutions.

Encourage Talk in Maths… but HOW???

Create and maintain a positive risk-free learning environment

Introduce Ground rules for Talk and keep reinforcing and practising them�

Talk Moves Group Roles

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Activities/ Tasks to talk!

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Vocabulary and ways to express ideas

Model Mathematical Thinking and Questioning

Should

we… ?

Have you noticed that…?

I agree with you because…

There are five academically productive ‘talk moves’:

1. Waiting: Using wait time
2. Revoicing. Saying in your own words what another student has said.
3. Repeating: Asking students to restate someone else’s reasoning
4. Reasoning: Asking students to apply their own reasoning to someone else’s reasoning.
5. Adding on: Prompting students for further participation.
6. Turn & Talk

These Talk Moves can be used in any subject during any learning session to facilitate productive discussions.

‘Talk Moves’ to Encourage Discussion

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Image Talk

What do you notice? What do you wonder?

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• What do you notice?
• What do you wonder?
• What maths can you see in this picture?
• Can you express this mathematically?
• What questions can you ask about this? How can you work it out?

Image Talk

Image Talk: Discovery on the Baking Tray

Number of doughnuts:

Counting, skip-counting, addition, multiplication, order of operations (more/ less, how many more, etc)

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Fractions, ratios, percentages

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Shapes and sizes (doughnuts and tray)

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Tray measurements:

If each doughnut has a diameter of x cm, workout the tray’s width, length, perimeter, area

Size of a box (or boxes) needed for these doughnuts

�Statistical investigation into doughnut preferences (PPDAC)

Number integration: What percentage of students prefer doughnuts with sprinkles?

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Financial Maths

If each doughnut costs $?, total cost = $?

If a box of 6 costs $?, cost per each doughnut $?

Do doughnuts with different toppings (eg, sugar glazing vs crushed nuts) cost the same?

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Image Talks

• What do you notice?
• What maths can you see in this picture?
• Can you express this mathematically?
• What questions can you ask about this? How can you work it out?

Maths Talk: Discovery in a Fruit Box 🍑

Fractions & Ratios

• Each row = ¼ of total
• Each column = ⅙ of total
• Dark:light fruit ratio
• Box dimensions ratio

Algebra & Patterns

• Cost per fruit = total cost ÷ 24
• Position pattern = row × column

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Basic Observations

• 4 × 6 array = 24 fruits + 3 = 27 total
• Or 4 x 7 = 28 - 1 = 27 nectarines
• Perfect example of rectangular arrays
• 2D and 3D Shapes (fruit, box)
• Simple ratio 4:6 = 2:3 (for part of the tray)
• Real-life data collection opportunity (be creative)
• Pattern recognition in arrangement

Measurements

• Unit of measurement (lengths, weight, etc)
• Estimate weight/size
• Perimeter
• Area per fruit ≈ 50cm² (think of layers)
• Symbols: ≈ vs =

Connecting Maths to Students’ Interests & Experiences

Image Talk

What do you notice?

What do you wonder?

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• I wonder how high the player jumped for this dunk.
• I wonder what the best angle is to score.
• I wonder what the chances are of making this dunk.
• I wonder what the probability is of landing 3 in a row.

Image Talk

What do you notice?

What do you wonder?

• I wonder how many egg cartons there are?
• I wonder how many eggs there are?
• I wonder how much weight it can hold before the eggs break if you sit on it!

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• What do you notice?
• What maths can you see in this picture?
• Can you express this mathematically?
• What questions can you ask about this? How can you work it out?
• How does this image relate to what we've learned in class?
• Find one maths idea for each of the following strands: number, geometry, algebra, measurement, statistics, and probability?
• If this image/ arrangement were part of a story, what would it be about? (integration with literacy)

Image Talk Guiding Questions

https://illustrativemathematics.org/resource-hub/

Image Talks: Conversation Prompts

25 glass gems

14 glass gems

The Reveal

51 glass gems

The Reveal

www.stevewyborney.com

Estimation: Think, Make Sense, Reason

Estimation: Think, Make Sense, Reason

Maths Talk Resources

• Find and select a Maths Image
• Add your image to this slide deck and anticipate all the possible ways students might solve it.
• What is your main purpose for using this image?
• Plan where you will fit this in your programme

Activity: Plan your Image Talk

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