Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

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Number and Operations

Finding Sums to Six

Pre-K-2
In this lesson, students discover the role of the additive identity and explore sums to six. They continue to complete their personal addition charts.
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Number and Operations

Some Special Sums

Pre-K-2
Students practice doubles and doubles-plus-one addition facts. They record their current level of mastery of the addition facts on their personal addition charts.
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Number and Operations

Addend Pairs to 12

Pre-K-2
Students practice their addition facts for sums up to 12 by playing a game. They add to their personal addition charts. Students are encouraged to practice the facts that they have not yet mastered. Finally, triangular flash cards help students practice addition facts.
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Number and Operations

What's Left?

Pre-K-2
Triangular flash cards and dice games help students practice addition facts. Students modify their "Addition Chart" to record the facts they know at the immediate-recall level.
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Number and Operations

Wrapping up the Unit

Pre-K-2
In this final lesson of the unit, students display their knowledge of properties of objects for sorting and creating patterns. They also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations.
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Algebra

Counting Back and Counting On

Pre-K-2
This lesson, which focuses on the counting model for subtraction, begins with reading a counting book. The students model the numbers as the book is read. Then they make a chain of links and write in vertical and horizontal format the differences suggested by adding and subtracting one link at a time from their chains. Finally, they draw a chain showing one link being taken away and write in two formats the difference it represents.
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Algebra

Taking Away Sets

Pre-K-2
This lesson encourages students to explore another model for subtraction, the familiar set model. Reading one of the many books that feature subtraction set the stage for this lesson in which the students write story problems, find differences using sets, and present results in a table. In the discussion of the table, they focus on the effects of subtracting all and subtracting 0.
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Algebra

Hopping Backward on the Number Line

Pre-K-2
In this lesson, students generate differences using a number line model. Because this model highlights the measurement aspect of subtraction, it is a distinctly different representation from the models presented in the previous lessons of this unit. The order property for subtraction is investigated. At the end of the lesson, children are encouraged to predict differences and solve puzzles involving subtraction.
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Algebra

Finding the Balance

Pre-K-2, 6-8
This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in equation form.
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Algebra

Finding Fact Families

Pre-K-2
In this lesson, students explore the relation of addition to subtraction with books and links. Then the children search for related addition and subtraction facts for a given number. They also investigate fact families, including those where one addend is 0 and where the addends are alike.