Teacher Sample

6th Grade Standard - 6.NS.B.4

Ratios & Proportional Relationships


Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).


When will all three of the guards work together again?

Students often confuse factors, multiples, GCF, and LCM. It is important that students get plentiful practice and are able to eventually define each of these terms. In The Castle Guard, two new guards join Clayton at his post, the Western Door. Clayton is a lonely guard who is grateful to have company, and he talks the ears off of the other two guards, who don’t have much to say. The two new guards eventually leave for the day, leaving Clayton alone. He is so pleased to have had company, he immediately wonders when they will all be together again and is eager to find out. The data provided is the work schedule for each of the three guards.

Day 1

The Math Simulator™

1. Immersion

  • Play The Castle Guard Immersion video, whole-class.
  • Restate the question: When will all three of the guards work together again?
  • Facilitate classroom discussion, ask students: "What do we need to know?"

2. Data & Computation

  • Print the Data Artifact, and distribute to students.
  • Allow students work time. Then ask students "Does your answer make sense?"
  • Consider using a sharing protocol to lead to mathematical insights and/or highlight misconceptions.
  • Allow students to revise their work.

3. Resolution

Answer: The three guards will work together in 20 days. (The LCM of 2, 4, and 5 is 20.)

Day 2

The Math Simulator™



1. Simulation Trainer

Practice Printable


1. Print and distribute the Practice Printable to your students.

2. Have students complete the Practice Printable. Consider using creative protocols.


Day 3

Practice Printable Cont'd


1. Have students complete the Practice Printable.

2. Have students complete the Student Reflection.

. Reflection-rubric

Day 4

Clicker Quiz


1. Have your students go to midschoolmath.com/clicker.

2. Click on Launch Clicker Quiz and note Clicker Quiz code.

3. Have students enter quiz code on their screens.

4. Launch Clicker Quiz.

5. Review Clicker Quiz results and prompt students to make connections to the Math Simulator.



Test Trainer Pro


15 minutes per day of the world class adaptive program "Test Trainer Pro"