THIRD GRADEEQUIVALENT FRACTIONS

STUDENT & PARENT GUIDE

LETTER TO PARENTS

Dear Parents and Caregivers,

As we continue to update you on math expectations of the Common Core State Standards, this

letter addresses the important, and for many children, difficult topic of fractions. In third grade,

children will begin to learn about equivalent fractions. This standard is a major expectation

and according to previous assessment data reviewed by the teachers, children often have

numerous misconceptions of part-whole relationships.

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by

reasoning about their size. It includes: Knowing that two fractions are equal if they are the

same size or can be placed at the same point on a number line; Children can name simple

equivalent fractions and explain why they are equal with the help of objects or drawings;

Knowing that whole numbers can be expressed as fractions For example, 3 = 3/1 and 6/6 = 1.

Being able to explain why, when fractions have the same denominator, one fraction is greater or

less than the other, and why, when two fractions have the same numerator, one is greater or

less than the other. Understand that such comparisons are valid only when the fractions refer to

the same whole.

C O N T I N U A T I O N O F L E T T E R

Your child is being asked to compare fractions using visual fraction models

and number lines. When comparing fractions, it is important to know that they

are comparing different parts from the same-sized wholes. For example, if I

am comparing ½ to 1/3, I need to make sure that I am referring to the same-

sized wholes. Then, I need to know the size of the parts as well. I can reason

that 1/2 is greater than 1/3 because half of one whole is greater in size than

1/3 of the same whole. In a number line, the length of 1/2 is greater than the

length of 1/3. Similarly, if I cut a ribbon into three equal parts and then cut the

same sized ribbon into four equal parts, then one piece of the ribbon cut into

thirds is longer in length than the one piece of the ribbon cut into fourths.

Fraction bars can be used to make this comparison easier to understand.

Here’s a visual representation:

Do you notice any patterns as you increase the number of parts you divide the

fraction bar into? What do you notice about the length or size of the part as the

number of parts increase? Ask your child to speculate and ask him/her if this is

always true, sometimes true, or never true. Ask for explanations and encourage the

use of math vocabulary when justifying arguments.

Equivalent fractions are fractions that have the same value, even if the number

of parts is different. Visually, here’s what fractions equivalent to one-half look like.

The first pizza is divided into 2 equal parts while the next, same-sized pizza is

divided into 4 equal parts and then the third, same-sized pizza is divided into 8

equal parts. You can go to this website to see how equivalent fractions are viewed

on the

number line. It’s interactive and fun! Just move the vertical bar to see the

equivalent fractions. www.mathsisfun.com/numbers/fraction-number-line.html

The unit on fractions is really challenging for most third-graders, but with

your

support and guidance, together we will be able to engage our children in

the

meaningful application of fraction concepts in real-world situations.

Fractions are

all around us. Let’s help our children realize the importance of the deep

understanding of this concept. This knowledge will provide a solid

foundation for

children to learn more challenging concepts in later grades.

USEFUL WEBSITES

http://www.mathsisfun.com/equivalent_fractions.html

http://www.aaamath.com/fra42ax2.htm

http://

illuminations.nctm.org/activitydetail.aspx?id=80

http://

www.sheppardsoftware.com/mathgames/fractions/memo

ry_equivalent1.htm

http://www.mathplayground.com/visual_fractions.html

http://www.coolmath4kids.com/fractions/fractions-04-

equivalent-01.html

MORE USEFUL WEBSITES

http://www.abcya.com/equivalent_fractions_bingo.htm

http://mrnussbaum.com/fractiondolphins/

http://www.fractionmonkeys.co.uk/

http://pbskids.org/cyberchase/math-games/melvins-make-

match

/

http://nlvm.usu.edu/en/nav/frames_asid_105_g_2_t_1.html

?open=activities&from=category_g_2_t_1.html

EQUIVALENT FRACTIONS

H T T P : / / W W W. Y O U T U B E . C O M / W A T C H ?V = W L 4 H I C Y M L K U

Click on the above link to view a YouTube video on equivalent fractions

V I D E O S O F H O W T E A C H E R R E M E D I AT E E Q U IVA L E N T F R A C T I O N S

http://www.bing.com/videos/search?

q=how+teacher+remediate+equivalent+fractions&

qpvt=how+teacher+remediate+equivalent+fraction

s&FORM=VDRE

PATCH TOOL – VIRTUAL M A N I P U L AT I V E S ( PAT T E R N B L O C K S )

http://illuminations.nctm.org/ActivityDetail.aspx?ID=27

Region Relationships:

1. How many green triangles are in one blue rhombus ?

2. How many green triangles are in one red trapezoid ?

3. How many green triangles are in one yellow hexagon ?

4. How many blue rhombuses are in one yellow hexagon ?

5. How many red trapezoids are in one yellow hexagon ?

EQUIVALENT FRACTIONS