Finding Equivalent Fractions

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SWBAT identify equivalent fractions while using a number line.

Big Idea

Using number lines and fraction strips helps students become familiar with benchmark fractions, equivalent fractions, and comparing fractions.


15 minutes

Students will be using a problem centered around a buddy rope.  The rope will be drawn on their paper (approximately 4 inches long) and they will use the rope (pseudo number line/fraction strip) to determine equal spacing along the rope.  This visual will help students understand the need for equal parts along partnered with developing an understanding of equivalent fractions.  As students are working through each of the problems, watch to see that they are separating the ropes into equal parts.  If students are having a difficult time “seeing” the parts, it would be a good idea to place a rectangle around the “rope” and have them use a fraction bar instead.

Before moving on in the lesson, allow students time to answer the questions on slide 5 on their own.  Once they’ve answered the questions, have the do a HUSPU to share and explore answers with a partner.

Question 1:  Students should see that ½ = 3/6 = 4/8.

Question 2:  Some students may see, through division, that 48/8 = 6 inches apart.

Question 3: For this question, I will be looking at students to identify that Ben has 1/3 of the rope and that 1/3 = 16 inches.  

Equivalent Fractions

40 minutes

Students will, again, be looking at fractions on the number line or fraction strips to determine equivalent fractions. 

In slide 6, the students will be looking at ½ and determining equivalent fractions.  I’m going to have student writing out the number sentence(SMP 2) because our goal is to get students to see the multiplicative relationship between equivalent fractions.  Students may want to mark on the visual and that’s ok if it  helps them to make the equivalent fraction.

Slide 7,  have them make marks where 1/3 and 2/3 would go.  Next, have them make a mark half way between 0 and 1/3 and half way between 2/3 and 1.  Ask them what these fractions would be called.  Again, if students have difficulty seeing this, have them make a rectangle around the number line to see the parts easier.

 Ask them what fractions are the same as 1/3, ½, and 2/3? (SMP 7)

Again, have them make marks half way between all the other marks.  Ask them to label the new marks. (twelfths)

Now have them write 3 number sentences.  For example ½ = 3/6.  (SMP 6)


The next slide has 2 fractions shown.  The question is asking the students to determine the distance between 3/5 and 7/10. Before letting them try this out, I’m going to tell them that the distance means the same as equal parts.  So if you want to find the distance between 1/6 and 2/6 there is a 1/6 distance between the two fractions.  If students are having difficulty determining the distance, have them mark out fifths and mark out tenths.  They should be able to determine that there is 1/10 in between the two numbers on the number line.

Have the students write 3 number sentences to show equivalent fractions.  For example 3/5 = 6/10.


20 minutes

The question for the NHT will connect the learning for today and apply it to some real world scenarios.  Each problem has the students looking at equal parts and determining and equal fraction.  I like to use the activity because it requires each student to make sense of the problem on their own (SMP 1) and then be able to share and explore solutions with the other members at their table (SMP 3).

Students will be working with white boards to show their solutions.

There are only 4 problems for this activity because each problem will require them to make a visual and state their answer using the visual.  Some students may be able to use the strategy for finding equivalent fractions, but encourage them to visually represent to support their answer.


10 minutes

Students will be answer 3 questions about their learning.   Two of the questions revolve around finding equivalent fractions and the last one has them explaining what strategy they use to find the equivalent fractions.  I’m anticipating that the students that understand equivalent fractions will be able to say that they multiply the numerator and denominator by the same number to make an equivalent fraction and at this time, this is above and beyond what is needed.  I’m expecting for master that students will say that when using a number line, the markings that match up are equivalent because they land in the same location (or something like that!) (SMP 8)