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# 7. Understand that objects can be counted in different ways (C)

teaches Common Core State Standards CCSS.Math.Content.K.CC.B.4a http://corestandards.org/Math/Content/K/CC/B/4/a
teaches Common Core State Standards CCSS.Math.Content.K.CC.B.4b http://corestandards.org/Math/Content/K/CC/B/4/b
teaches Common Core State Standards CCSS.Math.Practice.MP6 http://corestandards.org/Math/Practice/MP6

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Lesson objective: Understand that the number of objects arranged in a line, array, or circle, is the same no matter how it is counted.

Students bring prior knowledge of the relationship between numbers and quantities by connecting counting to cardinality (the idea that the last number name said tells the number of objects counted) from K.CC.4b (Grade K, Unit 2 & 3). This prior knowledge is extended to new arrangements as students count objects in different configurations. A conceptual challenge students may encounter is thinking that the number of objects changes as the configuration changes. (For example, as objects are more spread out, children often think there are more objects).

The concept is developed through work with line, array, and circle configurations, which supports students with ordered representations as they build the concept that the number of objects in a set stays the same even when the arrangement changes.

This work helps students deepen their understanding of equivalence as they notice that the number of objects stays the same in different configurations.

Students engage in Mathematical Practice 6 (Attend to Precision) as they count accurately. Teachers model for students how to organize their objects and count in a sequence.

Key vocabulary:

• circle
• count
• organize
• ten frame

Special materials needed:

• counting objects such as cubes, blocks, pennies, or counters
• double ten frame
• story mat
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