Image Talks
From Multiplicity Lab Northwestern
Never Say Anything A Kid Can Say
~ Steve Reinhart
How to use these slides
One Talk is 2 slides in length.
The first is the image, the second is the prompting questions to ask and the Big Idea that is at the heart of the Talk.
In the notes on each slide you will find an extension activity
You can begin every slide by asking What do you notice? What do you wonder?
Ask
How many cubes are in this solid?
How do you know?
How did you count the cubes you cannot see?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing with shapes
Ask
How many do you see?
How do you see them?
How do you know?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting number and quantity
Composing and decomposing number
Connecting area and multiplicative thinking
Ask
What do you notice?
What’s happening in this image?
What patterns do you see?
What does it make you wonder?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Sorting, organizing, and using attributes
Ask
Are there more buffalo in the water or out of the water?
How do you know?
What do you notice that could help you decide?
Big Ideas
Seeing mathematics in the world
Decomposing and using benchmarks to estimate
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Connecting quantity and number
Composing and decomposing number
Sorting, organizing, and using attributes
Using units to count, measure, and compare
Ask
What do you notice?
What stands out to you? Why?
What do you wonder?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Using units to count, measure, and compare
Ask
What’s missing?
What shapes could fill the empty space?
How do you know?
What do you notice that could help you?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Ask
How many cubes are in this solid?
How do you know?
How did you count the cubes you cannot see?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing with shapes
Ask
What’s missing?
What shapes could fill the empty space?
How do you know?
What do you notice that could help you?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
What do you notice?
What stands out to you? Why?
What do you wonder?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Connecting quantity and number
Composing and decomposing number
Sorting, organizing, and using attributes
Using units to count, measure, and compare
Ask
What patterns do you see?
How do you see them?
What shapes do you see?
How do shapes or lines repeat?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing shapes
Ask
About how many do you see?
How do you know?
What do you notice that can help you estimate?
What makes estimating hard?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Decomposing and using benchmarks to estimate
Composing and decomposing with shapes
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
About how many do you see?
How do you know?
What do you notice that can help you estimate?
What makes estimating hard?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Decomposing and using benchmarks to estimate
Ask
What do you notice?
What stands out to you?
Why?
What do you wonder?
What questions could you ask of this image?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Using units to count, measure, and compare
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
What patterns do you see?
How do you see them?
What shapes do you see?
How do shapes or lines repeat?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing shapes
Ask
What do you notice?
What stands out to you?
Why?
What do you wonder?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Using units to count, measure, and compare
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
Are there more green squares or orange squares?
How do you know?
How did you see it?
How could you figure it out?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Ask
What patterns do you see?
How do you see them?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Ask
What patterns do you see?
How could you extend (or add onto) this pattern?
Where would you add and what would you add? Why?
Big Ideas
Attending to and using structure
Ask
What do you notice?
What stands out to you?
Why?
What do you wonder?
Big Ideas
Seeing mathematics in the world
Connecting number and quantity
Sorting, organizing, and using attributes
Using units to count, measure, and compare
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
What patterns do you see?
How could you extend (or add onto) this pattern?
Where would you add and what would you add? Why?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
How many do you see?
How you you know?
How do you see it?
What did you notice about the animals that helped you count?
Big Ideas
Seeing mathematics in the world
Composing and decomposing number
Ask
How many do you see?
What are you counting?
How did you count them?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting number and quantity
Composing and decomposing number
Using units to count, measure, and compare
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
Which is more?
How do you know?
How did you see it?
What did you notice that helped you compare?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting number and quantity
Composing and decomposing number
Ask
How could you organize?
What do you notice about the vegetables and fruits that could help you organize them?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Sorting, organizing, and using attributes
Ask
Where can you find an array?
Take a picture, sketch it, or bring it with you to show the array you found.
Bring back at least one example of an array.
Off you go!!
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting area and multiplicative thinking
Sorting, organizing, and using attributes
Ask
Where can you find a square?
You can take a picture, make a sketch, or bring objects to show.
Off you go!!
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Ask
Which is more?
How do you know?
How did you see it?
What did you notice that helped you compare?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting number and quantity
Composing and decomposing number
This picture shows 6
Where do you see 6 in this picture?
Ask
Where else can you find 6?
You can take a picture, make a sketch or bring objects to show.
Off you go!
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting number and quantity
Composing and decomposing number
Ask
What do you notice?
What do you notice about the different parts of this image?
What relationships do you see?
What do you wonder?
Big Ideas
Connecting number and quantity
Sorting, organizing, and using attributes
Using units to count, measure, and compare
Ask
Which is more?
How do you know?
How did you see it?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Using units to count, measure, and compare
Ask
What’s missing?
What shapes could fill the empty space?
How do you know?
What do you notice that could help you?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Ask
What do you notice?
What stands out to you?
What relationships do you see?
How can you describe those relationships?
What do you wonder?
Note: For younger students, the rods can be conceived of as representing whole numbers, but for students in older grades, you can focus on part-whole fractional relationships. Even young students may also point out relationships of half, third, or quarter.
Ask
What patterns do you see?
How do you see them?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
About how many do you see?
How do you know?
What do you notice that can help you estimate?
What makes estimating hard?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Composing and decomposing number
Decomposing and using benchmarks to estimate
Connecting area and multiplicative thinking
Ask
How many do you see?
How do you see them?
What do you notice that is helping you to count?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Connecting number and quantity
Composing and decomposing number
Connecting area and multiplicative thinking
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
What patterns do you see?
How do you see them?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Ask
What’s missing?
What shapes could fill the empty space?
How do you know?
What do you notice that could help you?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Ask
What do you notice?
What stands out to you?
What relationships do you see?
How can you describe those relationships?
What do you wonder?
Note: For younger students, the rods can be conceived of as representing whole numbers, but for students in older grades, you can focus on part-whole fractional relationships. Even young students may also point out relationships of half, third, or quarter.
Big Ideas
Attending to and using structure
Connecting quantity and number
Composing and decomposing number
Using units to count, measure, and compare
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
What patterns do you see?
How could you extend (or add onto) this pattern?
Where would you add and what would you add? Why?
For Grades 1 and up: How many dots would there be then?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
About how many blocks are there?
How do you know?
What do you notice that can help you estimate?
What makes estimating hard?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Decomposing and using benchmarks to estimate
Composing and decomposing with shapes
Ask
What patterns do you see?
How could you extend (or add onto) this pattern?
Where would you add and what would you add? Why?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Ask
What patterns do you see?
Where do you see them?
What do you notice repeats?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Composing and decomposing with shapes
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Sorting, organizing, and using attributes
Ask
Which is more?
How do you know?
How did you see it?
What did you notice that helped you compare?
Big Ideas
Attending to and using structure
Composing and decomposing number
Ask
About how many do you see?
How do you know?
What do you notice that can help you estimate?
Big Ideas
Seeing mathematics in the world
Attending to and using structure
Composing and decomposing number
Decomposing and using benchmarks to estimate
Connecting area and multiplicative thinking
Ask
How could you organize the dice?
What questions could you answer by organizing the dice that way?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Link:�https://bpb-us-e1.wpmucdn.com/sites.northwestern.edu/dist/1/5269/files/2022/08/DI.049-Organize.pdf
Ask
What’s missing?
What shapes could fill the empty space?
How do you know?
What do you notice that could help you?
Big Ideas
Attending to and using structure
Sorting, organizing, and using attributes
Composing and decomposing with shapes
Ask
How many cubes are in this solid?
How do you know?
How did you count the cubes you cannot see?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing with shapes
Ask
How many squares are shaded?
How do you know?
How did you see it?
How could we represent what you saw with numbers and symbols?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing shapes
Ask
What patterns do you see?
How could you extend (or add onto) this pattern?
Where would you add and what would you add? Why?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
Are there more orange fish or striped fish?
Are there more total stripes or total spots?
How do you know?
What do you notice that can help you decide?
Big Ideas
Seeing mathematics in the world
Connecting number and quantity
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
How many?
How do you know?
How do you see it?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
What patterns do you see?
How could you extend (or add onto) this pattern?
Where would you add and what would you add? Why?
For Grades 3 and up: How many dots would there be then?
Big Ideas
Attending to and using structure
Composing and decomposing number
Sorting, organizing, and using attributes
Ask
Are there more red squares or green squares?
How do you know?
How did you see it?
How could you figure it out?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Are there more green squares or orange squares?
Ask
Are there more green squares or orange squares?
How do you know?
How did you see it?
How could you figure it out?
Big Ideas
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Which is More?
Ask
Which is more?
How do you know?
How did you see it?
What did you notice that helped you compare?
Big Ideas
Attending to and using structure
Composing and decomposing number
How many squares are missing?
Ask:
How many squares are missing?
How did you see it?
How could you figure it out?
Big Ideas:
Attending to and using structure
Composing and decomposing number
Connecting area and multiplicative thinking
Composing and decomposing with shapes