Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions (e.g., by using a visual fraction model). Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Add and subtract mixed numbers with like denominators (e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction).
Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators (e.g., by using visual fraction models and equations to represent the problem).
Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
4th Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of addition and subtraction of whole numbers and fractions. (A, B, and C part of the standard)
Report Card Measurement Topic:Demonstrates understanding of patterns, expressions, equations, and algebraic thinking. (D part of the standard)
3rd Grade Students Learning 4th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of addition and subtraction. (A, B, and C part of the standard)
Report Card Measurement Topic:Solves one and two-step word problems with any operation. (D part of the standard)
Learning Targets
Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).
Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add and subtract fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.
About the Math
Addition and subtraction of fractions with like denominators can be solved using an algorithm of adding or subtracting the numerators and keeping the same denominator. However, prior to this, students need instruction on the conceptual understanding of adding and subtracting fractions and what a reasonable answer looks like. Questions such as "will the answer when you add 7/8 + 3/8 be more or less than a whole and why?" should be part of instruction. Concrete materials should be used to introduce addition and subtraction prior to moving to the algorithm.
Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
Students need to see that a fraction can be decomposed just like whole numbers. There are many different ways to decompose a fraction. Understanding this helps students see the value of fractions and enhances their fraction sense. 7/10 = 1/10 + 1/10 +1/10 + 1/10 +1/10 + 1/10 + 1/10 or 3/10 + 3/10 + 1/10 or 5/10 + 2/10 or 4/10 + 2/10 + 1/10.
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
When adding or subtracting fractions, the values must refer to the same-size whole with the same number of partitions. This is also thought of as common denominators. In fourth grade, students only work with addition and subtraction of fractions with like denominators.
Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).
Addition and subtraction of fractions can be represented by a variety of models. Students should also represent addition and subtraction of fractions on a number line. Students should justify their sums and differences with models and connect that work to their equations. In time, students can work solely with the symbols/equations.
Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add and subtract fractions and mixed numbers with varied strategies.
A mixed number is a whole number and a fraction. Students need to see that 3 ¼ is the same as 3 + ¼. This can be connected to the previous standard of decomposing fractions. This understanding can be reinforced through the representations students use to add and subtract mixed numbers. Like other understandings, students should work with varied models including pattern blocks, Cuisenaire rods, and fraction tiles.
Solve word problems with adding and subtracting fractions and mixed numbers.
Students should represent problems with diagrams or drawings before attempting to solve. Bar diagrams or part-to-whole models are good for reinforcing this understanding. Students can then use tools to represent the computation with fractions as needed. Students should not rely on key words for finding the solution to these problems.
Essential vocabulary for this standard includes unitfraction, fraction, numerator, and denominator.
Progression of Standard within Grade 4
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Compose and decompose a fraction (i.e. 7/12 = 4/12 + 1/12 + 1/12 + 1/12).
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
Represent addition of fractions with varied models (including a number line).
Represent subtraction of fractions with varied models (including a number line).
Represent addition of mixed numbers with varied models.
Represent subtraction of mixed numbers with varied models.
Add fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.
Describe that adding and subtracting of fractions must refer to the same size whole and having like denominators.
Represent addition and subtraction of fractions with varied models (including a number line).
Represent addition and subtraction of mixed numbers with varied models.
Add and subtract fractions and mixed numbers with varied strategies.
Solve word problems with adding and subtracting fractions and mixed numbers.
These tasks can be used with small group or whole group instruction.
4.NF.3a
Why is ¼ + ¼ not equal to 2/8?
Will 6/10 + 6/10 be greater than one whole? Explain how you know.
How can you figure out what ¼ + ½ is without finding a common denominator? Explain how you did found the answer.
Decompose 11/12 in 3 different ways.
Esther ate ¾ of a small pizza on Monday and she ate ¼ of a large pizza on Tuesday. She says that she has eaten a whole pizza. Is she correct? Why or why not? Explain your answer.
4.NF.3b
Use fraction tiles or towers to build the fraction 1 5/6. Allow students to decompose or break apart the fraction manipulatives into different parts. Create a recording of the different ways the fraction can be decomposed. Continue the task using a different fraction.
Use fraction tiles or towers to create a fraction that has been decomposed into several parts. Students should write the repeated addition expression and identify the fraction that is created from the decomposed parts.
How many ways can you decompose 7/8? Show your representations.
What set of numerators can you find to make this equation true? Is there a different answer? 5/10 + 1/10 + 4/10 = /10 + /10 + _/10
Lily is having a sleepover with 2 friends. They order one party size submarine sandwich and it is cut into 12 equal parts. They eat the entire sandwich, but each person has a different number of parts. What is one way the sandwich was shared? Write an equation to represent your answer equal to 12/12. Is there a different way the friends could have shared the sandwich?
Play “Can You Get There In ? Jumps.” Using a number line, give students a fraction such as 10/12. Ask students to get there in 3 jumps on the number line. One answer might be 2/12, to 5/12, to 10/12 and can be represented by 2/12 + 3/12 + 5/12. Then ask if they can get there in 4 jumps?
4.NF.3c
If the sum of two mixed numbers is 6, what could the two addends be?
How can you use addition to solve 4 1/3 - 2 2/3?
Is the sum of 4 ⅖ + 2 ⅘ over or under 7? Explain why or why not.
Is the difference of 5 ⅔ - 3 ⅓ over or under 2? Explain why or why not.
How can you demonstrate how 4 ½ is equal to 9/2? Use models, drawings and/or equations to explain your thinking.
Write two problems that have a difference of 3 4/10?
4.NF.3d
At noon, the bakery had 1 whole pumpkin pie and 5/12 of a pumpkin pie available to sell. At the end of the day, 3/12 of a pie was left. How much pumpkin pie did the bakery sell during the afternoon?
Shelly needs 1 ⅜ cups of oats for a cookie recipe. How many cups of oats does Shelly need if she is tripling the recipe? (This question is not exclusive to multiplication of fractions, repeated addition can be used)
The answer is 5 ⅙, write a story problem involving addition and/or subtraction to result in this answer.
Jashae has 3 ¾ foot of yarn. She uses 1 ¼ foot of the yarn to make a bracelet. Then she gave her sister 1 ¼ foot of yard for her bracelet. How much yarn does she have left? Represent this problem visually.
Don came home and found a fraction of a large pizza on the counter. He eats 3/8 of the pizza and now there is 2/8 of a pizza left. What fraction of the pizza was on the counter when he got home?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides.These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.