OLD Resources. The resources on this page have NOT yet been updated to align with the revised elementary mathematics TEKS. These revised TEKS were adopted by the Texas State Board of Education in 2005, with full implementation scheduled for 2006–07. These resources align with the original TEKS that were adopted in 1998 and should be used as a starting point only.

Clarifying Lessons

Grade 5: Multiple Towers

Lesson Overview

Students use interlocking cubes to build towers to represent factors of numbers and place the towers in the appropriate places on a Tower chart in order to look for patterns.

Mathematics Overview

Students identify factor pairs of whole numbers and use patterns in the factor pairs to identify prime and composite numbers.

Set-up (to set the stage and motivate the students to participate)

  1. Have the students build towers of cubes on a Tower Chart. Explain that these towers will be built using the directions on the Multiple Towers worksheet. (5.3B, C, D; 5.14D)
  2. Discuss the first steps
    • Put dark green cube on the multiples of 1. What are the multiples of 1? Why?
    • Put a light green cube on multiples of 2. How will you decide on which numbers to put the cubes? What do we mean by a multiple? Can you give other examples? (5.3B, C, D; 5.14D)
  3. Let partners work together, following the directions and answering the questions on the worksheet. As pairs finish their towers, ask them to write statements concerning prime numbers, composite numbers, or patterns of factors they notice from their towers. Ask students to predict what their observations might be if their tower chart were extended to 25. (5.5C; 5.15A, B)

Teacher Notes (to personalize the lesson for your classroom)

Guiding Questions (to engage students in mathematical thinking during the lesson)

  • What is your strategy for finding multiples? (5.3B, C, D; 5.14C, D)
  • Can you identify a pattern to help you? (5.5B, 5.14C, 5.16A)
  • What do you notice about your towers?
  • How can you use your towers to find factor pairs of the numbers?
  • What are the factor pairs of 6?
  • What are the factor pairs of 4?
  • What do you notice about the number of cubes of the towers on the numbers 1, 4, and 9? Why did this happen? If you extended your tower chart to 25, what are other numbers for which you would observe the same thing? Why?
  • Compare the towers for 2, 4, and 8. What do you notice? Why do you think this happened? If you extended your tower chart to include 16, how would this pattern extend? Explain.
  • How can you use your towers to decide if a number is prime? Composite? Why?
  • How can you communicate your findings so that someone else will understand them? (5.14A, B)

Teacher Notes (to personalize the lesson for your classroom)

Summary Questions (to direct students' attention to the key mathematics in the lesson)

To emphasize the use of multiples and factors to describe prime and composite numbers, ask questions such as:

  • Which numbers had the tallest towers? Why? (They have the most factors from 2 to 10.) Which colors were in them? (5.3B, C, D; 5.5C; 5.14D; 5.15A, B; 5.16B)
  • Which numbers had only one cube? Why? (5.3B, C, D; 5.5C; 5.14D; 5.15A, B; 5.16B)
  • Look at the towers that have a yellow cube, what do you notice about these towers? Did you notice that whenever you put a black cube on a number, it already had a blue cube on it? Why do you suppose that happened? (Because a number that is a multiple of 9 also always is a multiple of 3.) If you extended your tower chart to 16, what cubes would the 16th tower contain? (5.3B, C, D; 5.5C; 5.14D; 5.15A, B; 5.16B)
  • What happened when you removed the towers and tried to put them back on correct numbers? What did you do to try to figure out where the tower might be placed? Did anyone try anything different? How did it work? (5.3B, C, D; 5.5C; 5.14D; 5.15A, B; 5.16A, B)
  • Did you discover anything else from the activity that we have not already discussed? (5.16A, B)

Teacher Notes (to personalize the lesson for your classroom)

Assessment Task(s) (to identify the mathematics students have learned in the lesson)

  • Give students a number between 1 and 100 and have them identify all of its factors, telling whether it is prime or composite.
  • Have students write everything they know about prime numbers and about composite numbers.
  • Have students identify three patterns they observed in their towers (e.g., everything with a brown cube also has a blue, a light green, and a dark green cube) and record them in their math journals.

Teacher Notes (to personalize the lesson for your classroom)

Extension(s) (to lead students to connect the mathematics learned to other situations, both within and outside the classroom)

  • Have students predict what will happen if they extended their towers chart. Test their predictions.
  • Have students predict which numbers will have tall or short towers and test their predictions.

Teacher Notes (to personalize the lesson for your classroom)