Fifth Grade - Pearson Assessments
Concrete to Algorithm Adding and Subtracting Fractions with Like Denominators
Materials: pattern blocks (yellow hexagons, red trapezoids, blue rhombi, and green triangles) Recording Sheet, SmartBoard file (MATH_4_A_2 ADD SUBTRACT LIKE DENOMINATORS SMARTBOARD 2014_RES)
Vocabulary: numerator, denominator, part, total, sum, difference, rename, lowest term, simplify, mixed number, whole, improper fraction
Slide 1: The purpose of this slide is to show students there is more than one way to represent a value with fractions. Students will use the TEKS 4.3B (decomposing a fraction in more than one way into a sum of fractions with the same denominator.)
By writing the fraction in multiple ways, students will better be able to simplify fractions.
Slide 2:
Have students manipulate the pieces on the SmartBoard to find the value of each.
(green triangle = [pic] , blue rhombus = [pic] , and the red trapezoid = [pic])
Guided Practice Example 1 (Addition):
Slide 3:
Begin the Four-Step Problem-Solving Process. What would the Main Idea be? (fractions pencils give away)
What details do they give us? (Package has 6 pencils, he gave away[pic] to brother and [pic] to sister)
Let’s use the pattern blocks to act out our story.
What do you think we will use to represent the whole package? Why? (yellow hexagon because we have assigned it the value of 1 whole)
What action is taking place in the story? Why? (Put together- Addition because we are seeing what fraction of the pencils were given away. Since he gave some to his brother and some to his sister we would put those fractions together to find how many he gave away.)
What expression would we write to represent this action? ([pic] + [pic] )
What other pattern blocks will we be using? Why? (green triangles because the story talks about sixths and it takes 6 triangles to fill the whole yellow hexagon.)
Have students use their pattern blocks to represent the [pic] and [pic] .
Explain to students that now that we are solving our expression, we will be writing it vertically.
[pic]
+ [pic]
[pic]
Students would then simplify the fraction with prime factorization to see that [pic] = [pic] .
How: Added the numerators and kept like denominator the same.
Simplified the fraction with prime factorization.
Guided Practice Example 2 Subtraction (Take Away):
Slide 4:
Begin the Four-Step Problem-Solving Process. What is our main idea?
(Fraction of students still standing in line?)
What details does our story give? (6 students in line, [pic] went in theater)
What action is taking place in the story? Why? (Take-away because we are seeing what fraction of the line is left)
What expression would we write to represent this action? (1 - [pic] )
Since our story is about taking away [pic] of the students, we want to find how many [pic]’s it takes to make the whole line of students. Have students start with a yellow pattern block to represent the whole line.
They will then replace the yellow hexagon with six triangles to show that 1 = [pic] .
Discuss how: 1 [pic]
- [pic] can be replaced with - [pic]
Remove 2 sixths to represent [pic] of the students that went into the theater.
[pic]
- [pic]
[pic]
Students will then need to simplify [pic] to [pic] using prime factorization.
How: Renamed 1 as [pic]
Subtracted [pic] from [pic] to get [pic] .
Simplified [pic] to [pic] with prime factorization.
Guided Practice Example 3 Subtraction (Missing Part)
Slide 5:
Begin the Four-Step Problem Solving Process. What is the main idea? (Fraction of pieces were blueberry?)
What are the details? (6 Jolly Ranchers, [pic] watermelon, [pic] cherry, remaining blueberry)
What action is taking place in the story and why? (Missing Part (subtraction) because we know the whole, and two flavors or parts, and are looking for the other flavor or part.)
What expression can we write to represent this action? (1 - [pic] - [pic] )
Let’s start by putting together the parts we know.
What expression represents the fraction of the candy that we know the flavor of?
([pic] + [pic] )
Explain that when we are solving, we will write it vertically.
Start with the yellow hexagon representing the whole (all 6 Jolly Ranchers). When we try to label the flavors we see that we need to trade the whole (yellow hexagon) for 6 equal parts (green triangle) showing that 1 = [pic] .
Now we can label 1 of the sixth pieces as watermelon and 3 of the sixth pieces as cherry.
Since we know two of the parts, [pic] and [pic] , let’s put those together first.
[pic]
+ [pic]
[pic]
What will our next step be? (Subtract [pic] from [pic] )
How many sixth pieces remain? (2) So what fraction does this represent? ([pic])
[pic]
- [pic]
[pic]
What flavor is the remaining pieces of candy? And what fraction represents this? (blueberry is [pic] of the candy.)
Can this fraction be simplified? (Yes) How would we do this? (use prime factorization to rename it in lowest terms.)
[pic] = [pic]
How: Added [pic] and [pic] and subtracted from [pic]
Guided Practice Example 4 Subtraction (Compare):
Slide 6:
Begin the Four-Step Problem Solving Process. What is the Main Idea? (How much further did Russell run than Jan?)
What are the details? (Jan ran [pic] and Russell ran [pic] )
What action is taking place in the story and why? (compare (subtract) because we are seeing how much further one person ran than the other.)
What expression can we write to represent this? ([pic] - [pic] )
When comparing fractions, students can build the 2 models and compare them.
Simplify [pic]= [pic]
How: Subtracted [pic] from [pic] to get [pic]
Simplified [pic] to [pic]
Guided Practice Example 5 Addition using Mixed Numbers
Slide 7:
[pic]
Begin the Four-Step Problem Solving Process. What is the Main Idea? (pizza eaten on Sat. and Sun.)
What details does the story give us? (Sat.-1[pic] , Sun.- 1[pic] )
What action is taking place in the story and why? (Put Together – Addition because they want to know Saturday and Sunday.)
What expression can we write to represent this? (1[pic] + 1[pic] )
Use the pattern blocks to represent these amounts.
Pull yellow wholes together and blue thirds together.
Show students how to add these vertically.
1 [pic]
+ 1 [pic]
2 [pic]
Now arrange the [pic] in wholes and parts.
And this makes 1 whole +[pic]. Now add the 1 whole to the existing 2, making 3 wholes and [pic].
Record and simplify. 2 [pic] = 3[pic].
Guided Practice Example 6 Subtraction using Mixed Numbers
Begin the Four-Step Problem Solving Process. What is the Main Idea? (H. M. bread left?)
What are the details? ( baked-4, ate - 1[pic])
What action is taking place in the story and why? (Take away – Subtraction because they started with 4 and ate 1[pic] and want to know what is left?)
What expression can represent this? (4 - 1[pic] )
Use the pattern blocks to represent the 4 loaves of bread.
Since her family ate 1 [pic] of the bread she baked, we will need to take away 1[pic] . Discuss with students that we are able to take 1 whole loaf away.
Are we able to take [pic] away from the 3 remaining loaves? (yes, we need to change one of them into halves so we can take [pic]away.)
Now we can take away 1[pic] .
This is how the work should be shown vertically.
Guided Practice without Models
1. Marcy poured 1 cup of hot water in a measuring cup. She used [pic] cup of the hot water in making her dessert. How much hot water was left in the measuring cup?
2. Dora’s family bought 1 bag of oranges. If the family ate [pic] of the bag of oranges, what fraction of the oranges remained?
3. Jonathan has a bag of colored marbles. There are 3 different colors in his bag. When he studied them, he found that [pic] of the marbles were blue. What fraction of the marbles were NOT blue?
4. Lisa ran 10 [pic] miles on Saturday. On Sunday she ran 5[pic] miles. How much farther did she run on Saturday than on Sunday?
5. Michael fed his dog [pic] cup of dry dog food twice each day. What is the total amount of dog food he fed his dog in three days?
6. Nancy watered her flowers three times each week. Each time she watered her flowers she used [pic] of a gallon. How much water did she use for the week?
-----------------------
Note: Students will be adding and subtracting fractions with like denominators with models that do not build to the number line. Students will be using the pattern blocks as their models. Students will be moving toward using the algorithm only, without models. Mixed numbers will also be used. For example, students will practice solving 4 - [pic] by renaming 4 to 3[pic] and then subtracting [pic]. In this lesson, when solving, the problem will be written vertically.
Reveal the examples under the shade if needed.
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