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IMA Parent – Level 2
Iterating and Partitioning with a Bar Model
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3. Iterating and Partitioning
What’s involved:
Seeing a quantity visually growing or shrinking by a factor (twice as long, half as long)
Understanding relationships between quantities
Why it matters:
Builds flexible thinking and decomposition of numbers
Lays the foundation for algebraic thinking
Helps students make sense of multiplicative situations
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4. Iterating and Partitioning: Bar Model
Activity
Show the child the model for the given quantity and ask them to copy it on their paper.
Ask the child to use what they know about the model/quantity they drew to generate the new model.
Finally, ask the child to use the sentence frame to describe what they did to complete their new model.
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5. Iterating and Partitioning
If the model below represents a unit of 4, draw a model for 14. Describe your process using the following sentence frame: “I iterated a unit of ____ ____ times to compose _____.” 4
Have the child draw the model on their paper, so they can use it to compose the new quantity.
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6. Iterating and Partitioning: Example Solution
If the model below represents a unit of 4, draw a model for 14.
I iterated a unit of _4_
_3 1 2 _ times
to compose _14_ 4 4 4 4 2
Note: Students will need to make sense of a unit of 2 being half of 4 either by partitioning into 2 units of 2 of 4 units of 1. 14
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7. Iterating and Partitioning
If the model below represents a unit of 6, draw a model for 36. Describe your process using the following sentence frame: “I iterated a unit of ____ ____ times to compose _____.” 6
Have the child draw the model on their paper, so they can use it to compose the new quantity.
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8. Iterating and Partitioning
If the model below represents a unit of 6, draw a model for 15. Describe your process using the following sentence frame: “I iterated a unit of ____ ____ times to compose _____.” 6
Have the child draw the model on their paper, so they can use it to compose the new quantity.
For this representation students could iterate 6, 2 ½ times, partition 6 into units of 3 and then iterate 5 times, or partitions 6 into units of 1 and iterate 15 times.
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Try other number sets If this (draw bar model) is ___ what would ___ look like?
Easy
Moderate
Hard
(6, 36)
(4, 10)
(18, 24)
(7, 35)
(6, 16)
(14, 21)
(8, 56)
(3, 11)
(10, 25)
(3, 21)
(5, 12)
(9, 12)
(4, 24)
(8, 10)
(15, 40)
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10. Iterating and Partitioning
If the model below represents a unit of 12, draw a model for 8. Describe your process using the following sentence frame: “I partitioned a unit of ___ into ___ units of ___ and counted ___ of them to compose ___.” 12
Have the child draw the model on their paper, so they can use it to compose the new quantity.
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11. Iterating and Partitioning: Example Solution
If the model below represents a unit of 12, draw a model for 8. 12
I partitioned a unit of _12_
into _3_ units of _4_ and counted _2_ of them to compose _8_. 4 8 8
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12. Iterating and Partitioning
If the model below represents a unit of 28, draw a model for 7. Describe your process using the following sentence frame: “I partitioned a unit of ____ into ____ units of ___.” 28
Have the child draw the model on their paper, so they can use it to compose the new quantity.
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13. Iterating and Partitioning
If the model below represents a unit of 64, draw a model for 16. Describe your process using the following sentence frame: “I partitioned a unit of ___ into ___ units of ___ and counted ___ of them to compose ___.” 64
Have the child draw the model on their paper, so they can use it to compose the new quantity.
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Try other number sets If this (draw bar model) is ___ what would ___ look like?
Easy
Moderate
Hard
(30, 6)
(96, 8)
(33, 9)
(42, 7)
(60, 12)
(36, 24)
(36, 9)
(5, 2)
(28, 21)
(48, 8)
(10, 4)
(84, 24)
(28, 4)
(15, 10)
(35, 15)
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