Lesson plan

8. Counting with different orders and arrangements (C)

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.MP3 http://corestandards.org/Math/Practice/MP3
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 is the same regardless of arrangement or the order counted.

Students bring prior knowledge of rote counting to 10 from K.CC.1. This prior knowledge is extended to counting sets in different orders or arrangements as students consider how changing the order or arrangement effects the count. A conceptual challenge students may encounter is thinking about part of a set and the entire set at the same time. 

The concept is developed through work with multi-colored counters, which can be counted in different ways and arrangements but still show the same number.

This work helps students deepen their understanding of equivalence because different arrangements of objects can be represented by the same count.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they consider multiple points of view and then through modeling the problem on their own, come up with a justification for their reasoning.

Key vocabulary:

  • arrange
  • counters
  • triangles

Special materials needed:

  • counters in 2 different colors