Sample Learning Goals for Grade 3

Remember: This list is not comprehensive! This is just a starting point!

Standard(CCSS numbering) / Learning Goal(s): Students will… / Sample Tasks/Activities
3.NF.1 (first part) / …understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.
(Example/paraphrase:
“The fraction 1/5 is the size of one piece when 1 whole thing is divided into 5 equal pieces.”
Unit fractions only at the beginning!) / Which of the following is 1/8 of the whole pizza?
Which piece of pie is written as“1/3” of the pie?
(More challenging): The circle is cut into different sized pieces. Which piece is 1/3 of the circle’s area? Which piece is 1/6 of its area?
Which of the stickers is 1/4 of a foot long?
Sketch a glass that is 1/3 full of lemonade.
Sketch 1/4 of a pizza.
Tina wants to give away 1/5 of a block of cheese. Draw a line across the block of cheese to show Tina where to cut.
Shade in 1/3 of the rectangle.
Rewrite each sentence, using a number in place of every number word: “Jim can only run half as fast as Bob.” “The police recovered one fourth of the stolen jewelry.”
Look at the picture, then circle the correct fraction to complete the sentence:
“The box is 1/2 1/4 1/5 full.”
Look at the picture, then write the correctfraction in the blank to complete the sentence: “The glass is _____ empty.”
Look at the picture, then write a sentence to describe the situation. Write number words/phrases using fraction notation. (E.g., “1/2 of the pizza has been eaten.”)
The length of each strip is a different fraction of one foot. Decide what fraction each represents by comparing it to a foot-long strip. Record your results.
Every coin (penny, nickel, dime, quarter, 50-cent piece, dollar coin) is a fraction of a dollar. What fraction of a dollar is each coin?Write your answers as fractions.
There are 12 inches in one foot. What fraction of a foot is one inch? (There are plenty of these:a foot is what fraction of a yard? ounce-pound? centimeter-meter? etc.)
3.NF.2.a / Represent a fraction 1/b on a number line by defining the interval from
0 to 1 as the whole and partitioning it into b equal parts. / Locate 1/2, 1/3, 1/4, 1/5, 1/6, and 1/8 on the number lines shown below.
Which of the following points is found at 1/6 on the number line?
3.NF.2.a / Recognize that each part has
size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. / (Show a number line that has been divided into b parts.) Look at this number line. What fraction is equivalent to the size of each part?
(Show a number line that has been divided into b parts and has the mark at 1/b highlighted or labeled.) Look at this number line. What fraction is located here?
3.NF.2.b / Represent a fraction a/b on a number line by defining the interval from
0 to 1 as the whole and partitioning it into b equal parts. / Locate4/5 (or any other a/b) on the number line shown below.
Which of the following points is found at 1/6 on the number line?
Draw a line that is 5/8 units long.
Use a ruler to draw a line that is 5/4 (or any appropriate a/b) inches long.
If this mark represents 2/3, which mark represents 1?
If this mark represents 8/5, which mark represents 1?
If this mark represents 2/5, which mark represents 2?
3.NF.2.b / Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. / (Show a number line that has been divided into b parts.) Look at this number line. What fraction represents the length from 0 to here? (where “here” is 9/10 or 12/5 or any a/b)
(Show a number line that has been divided into b parts and has the mark at a/b, such as 3/4 or 9/6, highlighted or labeled.) Look at this number line. What fraction is located here?
3.NF.3.a / Understand two fractions as equivalent (equal) if they are the same size, or the same point on the number line. / These two number lines have 0 and 1 marked equally far apart. Locate 6/8 on the top number line and 3/4 on the bottom number line. Is 6/8 larger, equal to, or smaller than 3/4? Explain.
Is there more than one name for every number on the number line? Explain.
What does it mean if two fractions with different names (symbols, to be precise) are the same distance from zero?
3.NF.3.b / Recognize and generate equivalent fractions. / Fold this piece of paper in half, one time. How many areas does the seam divide on the front of the page? What is the name of each of these parts compared to the whole front of the page? Now fold it again, horizontally or vertically (it doesn’t matter). How many parts are there now? What is the name of each part? How many of these smaller parts make one of the original parts? What can we conclude?
You have two strips of paper that are equally long. Cut one in three equally long pieces. Cut the other into six equally long pieces. Compare two of the smaller strips with one of the bigger strips. Sketch what you did and write an equation to describe the relationship between them (such as 1/3=2/6). Now comparefour of the smaller strips with two of the bigger strips…
Are 1/2 and 3/8 equivalent? Explain.
Are 3/4 and 6/8 the same length? Explain.
Express 2/3 in terms of sixths.
Each bottle holds 1/4 of a gallon. How many bottles are the same as 1/2 a gallon?
How many halves of a gallon are the same as two gallons?
How many thirds of a cup are the same as 4/3 cups?
Write three different fractions that are equivalent to 1/2 (or 2/3 or 4/5 or a/b).
The fraction 6/4 can be expressed with a denominator smaller than 4 and also with denominators larger than 4. Can you find a fraction equal to 6/4 that has a denominator less than 4? Can you find a fraction equal to 6/4 that has a denominator that is larger than 4? (can be done with numerators as well)
3.NF.3.b / Explain why the fractions are equivalent, e.g., by using a visual fraction model / Use a number line/double number line to show that 1/2 and 5/10 are equal.
Explain why 2/4 and 3/6 are equal. Draw an illustration as a part of your explanation.
Out of all the points that are highlighted on the double number line, which pairs are equivalent? Explain.
3.NF.3.c / Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers / Can you make a whole number out of fractions?Explain why or why not.
Count by 1/2. When does counting by 1/2 stop on a whole number?
Locate 1 on the number line. Now locate 3/3 on the same number line. What can you observe about 1 and 3/3?
How many halves/thirds/fourths/fifths/sixths/eighths does it take to make one whole?
Express 3 in terms of halves.
How many halves/thirds/fourths is two/three/four?
Put each fraction on the number line, and then explain which two are equivalent and why: 2/3, 1/4, 2/6, 4/6.
Which of the following is true? 2/2 = 2. 4/2 =2. 6/2 =2. Explain why.
Which of the following is true? 3/1 = 1. 3/1 =2. 3/1 = 3. Explain why.
Write the number four wholes in fraction form.
Write the number five as a fraction symbol with 5 as the numerator.
Joe drank 2 gallons of water this weekend. Jim drank 4/2. Who drank more? Explain.
3.NF.3.d / …be able to compare fractions with the same denominator but different numerators by reasoning about their size. / Which number is greater: 2/3 or 3/3?
Which number is less: 2/4 or 3/4?
Draw a picture of 2/5 of a pie and 4/5 of a pie. Use your picture to explain which fraction is less than the other.
If Rachel has 3/5 of a candy bar, and Donald has 4/5 of the kind of candy bar, who has more candy? Explain why.
Explain how a person can know whether 5/6 or 7/6 is larger.
Put the following numbers in order from least to greatest: 3/8, 1/8, 2/8, 4/8, 7/8.
Each carton is labeled according to how much orange juice is inside. Put the cartons in order from the smallest amount to the largest. (Labels have same denominator but different numerators.)
3.NF.3.d / …be able to compare fractions with the same numerator but different denominators by reasoning about their size. / Which number is greater: 3/4 or 3/5?
Which number is less: 2/6 or 2/8?
Draw a picture of 4/5 and 4/6. Use your picture to explain which fraction is greater than the other.
Put the numbers in order from least to greatest: 5/4, 5/3, 5/8, 5/2, 5/4.
Each carton is labeled according to how much orange juice is inside. Put the cartons in order from the smallest amount to the largest. (Labels have same numerator but different denominators.)
Which length is greater: 7/5 of a foot or 7/8 of a foot? Explain how you know.
3.NF.3.d / Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
(Remember: No mixed numbers until fourth grade) / Circle the point representing the smallest number.
Explain what it means that fraction is found to the left of fraction B.
Explain why 2/3 is more than 1/5.
Explain how you can tell which number/fraction is larger when you see both of them on the number line. Complete the sentence: “2/3 ___ 5/4.Explain your answer using the number line.
Decide which point represents the greatest number.Circle the point. Then, write a sentence such as “2/3 > 1/5 and 2/3 > 2/8” to expression your conclusion.

Compiled by Benjamin A. Smith () for use in the MAFS/CCSS Teaching Fractions Workshop for Santa Rosa County School District. Sample Learning Goals and Tasks are based on the Math Florida Standards and Common Core State Standards.