Number Sense – Compute Fluently with multi-digit numbers and find common factors and multiples

Greatest Common Factor

TEACHERS: Jennifer Mraz / SUBJECT: 6th Grade Math
STANDARD:
·  6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100.
OBJECTIVE (EXPLICIT):
·  Use tiles or chips to find the factors of numbers and determine the greatest common factor of the numbers.
KEY VOCABULARY: factors, common factors, greatest common factor / MATERIALS:
Square tiles or chips at least 12 per student and 24 per pair of students
ENGAGE (MAKE CONTENT AND LEARNING RELEVANT TO REAL LIFE AND CONNECT TO STUDENT INTEREST)
You are making 20 mint chocolate bars and 24 caramel pecan bars for
some gift boxes. If each box will contain exactly the same bars, what is
the greatest number of gift boxes you can put together? How many of
each bar will be in a gift box?
BEFORE / TEACHER WILL:
Ask students what a factor is? Have students discuss with a shoulder partner and be ready to share their answers. Teacher should lead the discussion so that students know that factors are numbers multiplied together to make a product.
Ask students what common factors are? Lead a discussion on common factors so that students understand that common factors are factors shared by two numbers. / STUDENT WILL:
Discuss with their shoulder partner the definition of a factor.
Discuss with their shoulder partner the definition of a common factor.
DURING / TEACHER WILL:
Model how to use tiles or chips to build a model for all the different ways to create the numbers 18 and 24 using rectangles or squares. (See examples below)
Ways to make 18:
1 row of 18
2 rows of 9
3 rows of 6
Draw pictures of the ways to make 18. (See examples below)
Ways to make 24:
1 row of 24
2 rows of 12
3 rows of 8
4 rows of 6
Draw pictures of ways to make 24.
Model how to circle the common factors in the two pictures: 1, 2, 3, 4, and 6 should be circled. (See examples below)
Ask students to identify the largest circled numer that both numbers shared. Lead a discussion with students to help them identify 6 as the greatest common factor. Ask students to locate the greatest number in a row the two rectangles have in common.(See examples below)
Pass out the greatest common factor worksheet and tell students to work with a partner to find the greatest common factor of each set of numbers by using tiles and drawing pictures.
Distribute the greatest common factor practice worksheet. (see linked worksheet)
Have students work with a partner to build and then draw the sets of numbers with their tiles. Instruct them to circle the common numbers and locate the greatest common number which will be the greatest common factor. / STUDENT WILL:
Use their tiles to follow along with the teacher to model the different ways to create 18 and 24 using rectangles or squares.
Ways to make 18:
1 row of 18
2 rows of 9
3 rows of 6
Draw pictures of ways to make 18.
Ways to make 24:
1 row of 24
2 rows of 12
3 rows of 8
4 rows of 6
Draw pictures of ways to make 24.
Circle the common factors in the two pictures: 1, 2, 3, 4, and 6 should be circled.
Identify the number 6 as the largest number in common between the two pictures drawn.
Work with a partner to build rectangles out of two sets of numbers and draw a picture of their build to list common factors and find the greatest common factor.
Work with a partner to build rectangles using pairs of numbers. Compare common configuration numbers and circle them. Discover the largest circled number in common.
AFTER / TEACHER WILL:
Ask students the engage question. You are making 20 mint chocolate bars and 24 caramel pecan bars for
some gift boxes. If each box will contain exactly the same bars, what is
the greatest number of gift boxes you can put together? How many of
each bar will be in a gift box?
Have students work in groups of 4 to answer the question. Remind them to use their tiles and draw pictures to help them solve the problem. Lead a discussion of possible answers. Ask students to explain their thinking to the class.
Ask students to write a paragraph describing how to find the greatest common factor of two numbers less than 100. / STUDENT WILL:
Work with a group of 4 students to solve the chocolate bar question. Use tiles and pictures to discover their answer.
Write a paragraph describing how to find the greatest common factor of two numbers less than 100.