Geometric Solids and Their Properties: Looking for Patterns

This is Lesson 3 of a 5 lesson series.  This lesson is an extension of lesson 2 and includes modeling and problem solving as well as the discovery of Euler's Formula.  It includes student questions and an assessment option. The student will use visualization, spatial reasoning, and geometric modeling to solve problems, and will discover Euler's Formula.

Standards & Objectives

Academic standards
CLE 3108.1.4
Move flexibly between multiple representations (contextual, physical written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to...
CLE 3108.4.5
Extend the study of planar figures to three-dimensions, including the classical solid figures, and develop analysis through cross-sections.
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
Learning objectives: 

Students will:

  • Skip count by twos, threes, fives and tens.
  • Find products by adding equal sets.
  • Explore the commutative property of multiplication.
Essential and guiding questions: 
  • What numbers did you say when you skip count by 2? By 5? By 3? By 10?
  • How can we show that 3 × 6 has the same product as 6 × 3?
  • What is similar about skip counting by 5 and adding 5 + 5 + 5? What is different?
  • How does knowing how to skip count by 2 help you skip count by 4?

Lesson Variations

Blooms taxonomy level: 
Extension suggestions: 
  • Say to students, "Let's skip count by 3 by singing the answers to the tune of "Are You Sleeping?" Is that easier or harder for you than just saying the words? [Singing slowly will make it easier for most students.]
  • You may wish to refer to Skip-Counting Songs for Multiplication for song ideas for various factors.
  • Move on to the next lesson, Looking for Calculator Patterns.


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