Math Manipulatives Lesson

Math Manipulatives Lesson Subject:​ Mathematics Unit:​ Fractions Title:​ Comparing and Ordering Fractions Grade: ​6 Strand: ​Number Sense and Numeration Time: ​60 minutes Curriculum Expectations: ● represent,compare,and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers,using a variety of tools (e.g.,fraction circles,Cuisenaire rods, drawings,number lines,calculators) and using standard fractional notation Instructional Procedure and Activities: Open ​(2-5 minutes): Begin by reviewing the prerequisite skills that students should have to be able to compare and order fractions (i.e. equivalent fractions). Do a few examples on the board as a class. Do some examples of how to properly use the fraction circles, or allow leader student to demonstrate. Body ​(35-45 minutes): We will start by comparing fractions with the same denominator (i.e. 73 v.s 74 ). We will then move onto comparing two fractions with different denominators. Start by using the fraction circles as a visual explanation and then move onto doing examples on the board. Explain that in order to compare fractions, they must have the same denominator. Therefore, you need to find an equivalent fraction where necessary (i.e. comparing 21 and 31 ; the common multiple of 2 and 3 is 6, so 1 3 1 2 3 2 2 becomes 6 and 3 becomes 6 ; 6 > 6 ). Students should be able to use their knowledge of equivalent fractions and common multiples to do this. Once the fractions have the same denominator, you can compare them to see which is bigger or smaller. The teacher will do a few examples on the board with the class and then have students come up to the board to do an example (about 4 at a time). Once students are more confident, we will move on to ordering a series of fractions. The process for ordering fractions is the same as comparing fractions, where the fractions all must have the same denominator. The teacher should do a few example on the board with the class and then again, have individual students come up to the board to do an example. Consolidation ​(10-15 minutes): Students will be placed into groups of 2-3 and be given a set of fractions circles. They will get a chance to explore and become familiar with the circles. The teacher may give prompts if students find themselves stuck or unsure (i.e. how many different ways can you make one complete circle using all different pieces?) Closing ​(3-5 minutes): Have each pair/ group write down 3 observations on a piece of paper about what they discovered while playing around with the fraction circles. The teacher will collect their written observations. Once they’ve handed in their paper, each student will be given the Comparing and Ordering Fractions worksheet. Prerequisite Concepts and Skills: ● Equivalent fractions ● Expressing fractions in improper and

Assessment and Evaluation:​ The Comparing and Ordering Fractions worksheet will be a way of formatively assessing students to see if they have

●

mixed form Common multiples/ factors

a grasp on the concepts covered in class.

Accommodations/ Modifications Accommodations ● Anchor charts with examples of equivalent fractions. ● Access to a fraction wall if additional manipulatives needed ● Positive peer grouping for students with diverse skills in order to perform reviews with the fraction circles. ● Provide individual quiet seating for students who request it during their activity. Modifications ● Students with modified instruction to the 4th and 5th grade will have to demonstrate their knowledge of equivalent fractions using only questions 1-6 on their worksheet, as the application portion is not yet required at this grade level. ● They will receive additional practice of expressing equivalent fractions using Math playground games at their grade level.

Considerations: Differentiated instructions ● “Chunk” worksheet for students with accommodation/ modified needs ● Have check in with students as they move through their worksheets onto each portion ( ex, 1-6, 6-9) ● Rotate during students exploration of manipulatives - with specific interest on students with collaborative skill support ● Students with memory anchor requirements will be strategically sat by these anchor charts ○ Additional anchor charts may be brought to individual desks if needed Extended activities (Early Finishers work ahead) ● Mathplayground -online free math games ● Demonstrate your equivalent fractions using pie chart technology on excel or google software. ● Allow students to choose between practicing the skill if needed or extending their knowledge with the additional challenge.

Required Materials/Resources: ● Fractions circles kits ● Comparing and Ordering Fractions worksheet ● Anchor charts equivalent fractions

References: OTF. ​Teach Special Education.​ Accessed March 2019 http://www.teachspeced.ca/ MathPlayground. ​Free Online Math Games. Accessed March 2019 https://www.mathplayground.com/grade_4_ga mes.html Ontario. (2005). ​The Ontario curriculum, Mathematica grades 1-8.​ Toronto: Ontario, Ministry of Education.

Reflection and Feedback:

Comparing and Ordering Fractions Using the fraction circles, answer the following questions questions in the space provided below. 1. Use the fraction circles to compare the following fractions. Circle the one in each pair that is bigger. a.

1 3

and

1 4

b.

3 5

and

2. Using the fraction circles, put together two

1 3

4 6

c.

3 4

and

5 8

pieces. Do the same thing with four

1 6

pieces. What do you notice about the two circles?

3. Order the following fractions from least to greatest:

1 2

,

2 3

,

2 8

,

3 5

4. How many different ways can you make a half? A third? A quarter? (Use the fraction circles to explore).

5. If you add

2 4

and

1 6

how much of the circle is left over?

6. How many tenths are in

7. Tamar’s team won

5 8

2 5

?

of their soccer games. Lilly’s team won

Which team won more game?

2 4

of their soccer games.

8. Mr. Burton’s class is having a bake sale fundraiser. They decide to sell slices of various pies. They have 10 pies in total and cut each pie into 8 equal slices. They sell 45 slices in the first hour of the bake sale. How many pies did Mr. Burton’s class sell in the first hour? Express your answer as both a mixed fraction and an improper fraction.

9. A survey was taken in the class of the top five sports that students enjoy. Volleyball accounted for

1 4

of the votes and soccer accounted for

3 8

. The remaining sports of

basketball, swimming, and tennis were all equal in amount. What fraction of the class enjoys the last three sports? What is the fraction for each sport?

Comparing and Ordering Fractions (Answer Key) Using the fraction circles, answer the following questions questions in the space provided below. 1. Use the fraction circles to compare the following fractions. Circle the one in each pair that is bigger. a.

1 3

and

1 4

b.

3 5

and

2. Using the fraction circles, put together two

1 3

4 6

c.

3 4

5 8

and

pieces. Do the same thing with four

1 6

pieces. What do you notice about the two circles? ​They are the same.

3. Order the following fractions from least to greatest:

1 2

2 3

,

,

2 8

,

3 5

>

2 8

,

1 2

,

3 5

,

2 3

4. How many different ways can you make a half? A third? A quarter? (Use the fraction circles to explore). ​(Answers may vary; i.e.

5. If you add

2 4

and

1 6

=

1 4

+

1 4

)

how much of the circle is left over?

6. How many tenths are in

7. Tamar’s team won

1 2

5 8

2 5

? ​4 tenths (4 x

1 10

1 3

)

of their soccer games. Lilly’s team won

Which team won more game? ​Tamar’s team ( 58 >

2 4

)

2 4

of their soccer games.

8. Mr. Burton’s class is having a bake sale fundraiser. They decide to sell slices of various pies. They have 10 pies in total and cut each pie into 8 equal slices. They sell 45 slices in the first hour of the bake sale. How many pies did Mr. Burton’s class sell in the first hour? Express your answer as both a mixed fraction and an improper fraction. ​5 58 or

9. A survey was taken in the class of the top five sports that students enjoy. Volleyball accounted for

1 4

of the votes and soccer accounted for

3 8

. The remaining sports of

basketball, swimming, and tennis were all equal in amount. What fraction of the class enjoys the last three sports? What is the fraction for each sport?

3 8

;

1 8

for each sport.

45 8