Common Factors
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students make observations about pairs of figures that each contain 6 and 10 squares. The height of each pair of figures changes, representing factors and common factors of 6 and 10, though students may not make this connection.
Launch
Display the image of the four pairs of figures from the Task Statement for all to see. Tell students to give a signal when they have at least one thing that is similar and one thing that is different. Give students 1 minute of quiet think time, and follow with a whole-class discussion.
Student Task
How are the pairs of figures alike? How are they different?
Sample Response
Sample responses:
Similarities:
- Each pair has a blue figure and a yellow figure.
- Each figure is made of small squares.
- Each yellow figure is made up of 6 squares. Each blue figure is made up of 10 squares.
Differences:
- Some pairs have rectangles, and some do not.
- Some pairs have L-shaped figures and some do not.
- The heights of each pair is going up by 1 every time: 2, 3, 4, 5
- The first pair with a height of 2 is the only pair with two rectangles.
- The pair with a height of 4 is the only pair without at least one rectangle.
Activity Synthesis (Teacher Notes)
The purpose of this discussion is to connect the pairs of figures to factors of 6 and 10. Ask students to share the things that are alike and different among the pairs of images. Record and display their responses for all to see. If possible, record their responses on the images where appropriate.
If not mentioned by students, discuss the following questions:
- “2 and 3 are both factors of 6. How is this reflected in the diagram?”
- “2 is a factor of both 6 and 10. How is this reflected in the diagram”
- “4 is not a factor of either 6 or 10. How is this reflected in the diagram?”
Remind students that a factor is one of two or more numbers that when multiplied together result in a given product. In this particular case, a factor is the height that will make a rectangle have a given area.
Standards
- 6.NS.4·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. <em>For example, express 36 + 8 as 4 (9 + 2).</em>
- 6.NS.B.4·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.<span> For example, express <span class="math">\(36 + 8\)</span> as <span class="math">\(4 (9 + 2)\)</span>.</span>
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Common Factors
5 min
Teacher Prep
Setup
Narrative
In this Warm-up, students make observations about pairs of figures that each contain 6 and 10 squares. The height of each pair of figures changes, representing factors and common factors of 6 and 10, though students may not make this connection.
Launch
Display the image of the four pairs of figures from the Task Statement for all to see. Tell students to give a signal when they have at least one thing that is similar and one thing that is different. Give students 1 minute of quiet think time, and follow with a whole-class discussion.
Student Task
How are the pairs of figures alike? How are they different?
Sample Response
Sample responses:
Similarities:
- Each pair has a blue figure and a yellow figure.
- Each figure is made of small squares.
- Each yellow figure is made up of 6 squares. Each blue figure is made up of 10 squares.
Differences:
- Some pairs have rectangles, and some do not.
- Some pairs have L-shaped figures and some do not.
- The heights of each pair is going up by 1 every time: 2, 3, 4, 5
- The first pair with a height of 2 is the only pair with two rectangles.
- The pair with a height of 4 is the only pair without at least one rectangle.
Activity Synthesis (Teacher Notes)
The purpose of this discussion is to connect the pairs of figures to factors of 6 and 10. Ask students to share the things that are alike and different among the pairs of images. Record and display their responses for all to see. If possible, record their responses on the images where appropriate.
If not mentioned by students, discuss the following questions:
- “2 and 3 are both factors of 6. How is this reflected in the diagram?”
- “2 is a factor of both 6 and 10. How is this reflected in the diagram”
- “4 is not a factor of either 6 or 10. How is this reflected in the diagram?”
Remind students that a factor is one of two or more numbers that when multiplied together result in a given product. In this particular case, a factor is the height that will make a rectangle have a given area.
Standards
- 6.NS.4·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. <em>For example, express 36 + 8 as 4 (9 + 2).</em>
- 6.NS.B.4·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.<span> For example, express <span class="math">\(36 + 8\)</span> as <span class="math">\(4 (9 + 2)\)</span>.</span>