North Adams Public SchoolsMath Expressions
Grade 5 Unit 1: Addition and Subtraction with Fractions(20 days)
In this unit, students study fractions and mixed numbers. They find equivalent fractions, compare fractions, and add and subtract fractions and mixed numbers. Students use models to represent addition and subtraction of fractions. Fraction bars, number lines, and area model representations help students understand concepts of fractions. Practice with pattern blocks, Cuisenaire rods, fraction bars and circles help all students achieve understanding of this critical concept.Establish a respectful classroom environment by using the suggested Math Talk and daily Quick Practice activities. Posters, charts, and other reference materials support student learning throughout the year. For a quick overview of important elements of the Math Expressions program, see this SlideShare presentation:
Big Idea 1: Equivalent Fractions
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect
MX Quick Quiz 1 Objectives (Day 6)
- 1A: Create equivalent fractions by multiplying or dividing numerators and denominators of given fractions by the same number.
- 1B: Compare fractions using a variety of strategies including rewriting them with a common denominator.
- 1E: Solve real-world problems.
Vocabulary
Benchmark / Equivalent / Multiplier
Common denominator / Estimate / Numerator
Common factor / Like and unlike denominators / Round
Denominator / Mixed number / Simplify
Day / Lesson / Student Learning Objective(s) / Notes
Tue.
9/8/15 / Unit 1 Lesson 1
Introduce the Math Board
MX pp. 1-6 /
- Find patterns in fraction representations on the math boards.
- Tell how unit fractions are used to build non-unit fractions.
Explain a unit fraction. Describe how they are used to build other fractions. / MathBoards today for work with fraction bars. Fraction poster is also needed.
TE p. 3 Connect finding an unknown addend to make a whole to their understanding of finding unknown addends in addition.
Wed. 9/9/15 / Unit 1 Lesson 2
Explain Equivalent Fractions
MX pp. 7-16 /
- Generate equivalent fractions
- Give examples of using a multiplier
- Use a number line to visualize equivalent fractions
TE p. 13 Use “simplify” instead of “reduce” as students may think “reducing” a fraction makes that quantity less.
Thu.
9/10/15 / Continue Lesson 2
Formative Assessment: Check Understanding TE p. 14
Explain how two fractions can be equivalent if they are made up of different numbers.
Fri.
9/11/15 / Unit 1 Lesson 3
Equivalent Fractions and Multipliers
MX pp. 17-24 /
- Tell how equivalent fractions relate to the multiplication table
- Use equivalent fractions to share a giant pizza
Explain how you can make several fractions equivalent to another fraction. / TE p. 23 Math Writing Prompt: Why is it always possible to unsimplify a fraction, but often impossible to simplify it?
This problem is given as a challenge problem but would be great discussion for all students.
Mon.
9/14/15 / Unit 1 Lesson 4
Strategies for Comparing Fractions
MX pp. 25-34 /
- Compare fractions with fraction bars and by reasoning about their size
TE p. 28 Teaching Note. Make this into a simplified chart or poster, so students can refer to it throughout the unit.
Tue.
9/15/15 / Continue Lesson 4
Formative Assessment: Check Understanding TE p. 32
Describe at least two strategies you can use to compare fractions. Give examples to illustrate each strategy. / TE p. 29 Differentiated Instruction: Cross-Multiplication. See For a kid-friendly explanation of why this method works for comparing fractions. They need to understand why it works, not just how.
Wed. 9/16/15 / Unit 1 Lesson 5
Fractions Greater Than One
MX pp. 35-42 /
- Represent fractions and mixed numbers with numbers and drawings
- Convert between fractions and mixed numbers
- 1A Create equivalent fractions by multiplying or dividing numerators and denominators of given fractions by the same number.
- 1B Compare fractions using a variety of strategies including rewriting them with a common denominator.
- 1E Solve real-world problems.
Use fraction manipulatives for students to show how unit fractions compose non-unit fractions and whole numbers.
Addition and Subtraction with Fractions Unit Plan
Big Idea 2: Addition and Subtraction with Fractions
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) (Major Content for grade 5)
5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect (Major Content for grade 5)
5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2,1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all beakers were redistributed equally. (Supporting Content for grade 5)
MX Quick Quiz 2 Objectives (Day 6)
- 1C: Add and subtract fractions with mixed numbers with like and unlike denominators.
- 1D: Make reasonable estimates of sums and differences of fractions and mixed numbers.
- 1E: Solve real-world problems.
Day / Lesson / Student Learning Objective(s) / Notes
Thu.
9/17/15 / Unit 1 Lesson 6
Add and Subtract Like Mixed Numbers
MX pp. 43-50 /
- Add and subtract mixed numbers with like denominators
Explain how you subtract two mixed numbers when the fraction part of the first number is less than the fraction part of the second fraction.
Tech G3-5: 1.18 Use age-appropriate internet-based search engines to locate and extract information, selecting appropriate key words. / TE p. 44 Suggestions for Math Talk through Solve and Discuss problems are included every lesson.
TE p. 47 Teaching Note Watch For! Students still revert to subtracting “up” when they are unsure what to do. Reinforce the language of subtraction. Have them say which number is the starting amount, what is being taken away from it.
Show students how to search for information related to what they are learning on the internet. Use the search bar in Chrome to find examples of 5.NF.1. When results appear, have students click images. Give students five minutes to work in pairs to find information about this standard. Have pairs discuss what other key words they could search to find information related to 5.NF.1. Share a few suggested terms.
Fri.
9/18/15 / Unit 1 Lesson 7
Add Unlike Fractions
MX pp. 51-60 /
- Use MathBoards to visualize finding common denominators to add unlike fractions
- Rename fractions and solve problems with addition of unlike fractions
Explain why common denominators are needed when adding fractions. / Adding (or subtracting) denominators continues to be the biggest trap for students learning fraction operations. Discussion, posters, examples of student work, See suggestions for helping students overcome this common misunderstanding at the website below:
Mon.
9/21/15 / Unit 1 Lesson 8
Subtract Unlike Fractions
MX pp. 61-66 /
- Use MathBoards to visualize finding common denominators to subtract unlike fractions
- Rename fractions and solve problems with subtraction of unlike fractions
Use an example to explain a method for subtracting fractions with unlike denominators. / Comparison problems are familiar to students with whole numbers. Write a simple comparison problem with small whole numbers for students to solve before starting with fractions.
Tue.
9/22/15 / Unit 1 Lesson 9
Solve with Unlike Mixed Numbers
MX pp. 67-74 /
- Solve word problems with mixed numbers
Give an example of when you would need to ungroup to subtract mixed numbers. / TE p. 68 Teaching Note. During discussion of methods, create a poster similar to what is included in the “What to Expect from Students” section. This reference chart can be used during Math Talk when students are explaining their work.
Wed.
9/23/15 / Unit 1 Lesson 10
Practice with Mixed Numbers
MX pp. 75-80 /
- Classify methods of finding a common denominator
- Practice adding and subtracting mixed numbers with unlike denominators
Make a list of important things to remember when adding and subtracting mixed numbers. / TE p. 80. Sports Connection. Do this with teams and have students compare the total points earned within a team and among the teams. Each team could make a poster with a short report and their data that could be part of a display of student work.
Thu.
9/24/15 / Unit 1 Lesson 11
Reasonable Answers
MX pp. 81-86 /
- Use benchmarks and rounding to estimate with fractions and mixed numbers
Tech G3-5: 3.3 Evaluate internet resources in terms of their usefulness for research.
Formative Assessment: Check Understanding TE p. 84
Explain a method for mentally estimating sums and differences of fractions and mixed numbers. Illustrate the method with examples. / TE p. 82 Review Benchmark Fractions. Make a chart like the number line given. If possible, laminate, so students can draw divisions to place fractions on it when deciding which benchmark it is closest to. This could be used as a 2-3 minute filler activity until students understand the concept.
Show students how to find the website below. Ask students how to use the website to find definitions for words. Students work in pairs to find and record definitions, examples, and illustrations of vocabulary words. After, discuss the website’s usefulness. What would you tell the web designer?
TE p. 86 Real World Connection. This would be another good display of student work using cutouts of various lengths that must be measured and ordered, then glued and labeled on a poster.
Fri.
9/25/15 / Unit 1 Lesson 12
Real-World Problems
MX pp. 87-92 /
- Solve word problems with addition and subtraction of mixed numbers
- Check to see if the answers are reasonable
Describe helpful strategies for solving word problems. / TE p. 88 Teaching Note. Throughout the Math Expressions program, students are taught a consistent problem-solving process.
- Interpret the problem.
- Represent the situation.
- Solve the problem.
- Check that the answer makes sense.
Mon.
9/28/15 / Unit 1 Lesson 13
Focus on Mathematical Practices / Skip this lesson / See for great problems that can be used in place of this lesson.
Tue.
9/29/15 / District Test 1
Assessment Examples
5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) (Major Content for grade 5)
5.NF.1 2014 MCAS #16 Short Answer 7/10
2/5 + 4/10 =
5.NF.1 2014 MCAS #19 Multiple Choice A
Sue needs to practice clarinet for 10 hours this week.
- On the first day of the week, she practiced for 1 ½ hours.
- On the second day of the week, she practiced for 1 ¼ hours.
- 7 ¼
- 7 4/6
- 8 2/6
- 8 ¾
5.NF.1 2013 MCAS #19 Open Response
Brenda is making tree costumes for a play. The list below shows the amounts of the different colors of cloth Brenda will use to make one tree costume.
3 5/8 yards brown cloth
2 ½ yards orange cloth
2/3 yards yellow cloth
- What is the difference, in yards, between the amount of orange cloth and the amount of brown cloth that Brenda will use to make one tree costume? Show or explain how you got your answer.
- What is the total amount of cloth, in yards, Brenda will use to make the leaves of one tree costume. Show or explain how you got your answer.
- What is the total amount of cloth, in yards, Brenda will use to make two tree costumes? How or explain how you got your answer.
5.NF.1 PARCC End of Year Test #21 Part A: D, Part B: D
Ammaar put 4/7 of the money he earned in the bank. He spent 1/3 of the money on a book.
Part A
Which expression can be used to find the difference between the fraction of money Ammaar put in the bank and the fraction of money he spent on the book?
- 4/10 – 1/10
- 8/10-7/10
- 4/21-1/21
- 12/21-7/21
What is the difference between the fraction of money Ammaar put in the bank and the fraction of money he spent on the book?
- ¾
- 1/7
- 3/10
- 5/21
5.NF.1 PARCC Performance Based Assessment C, F
An expression is shown.
5/6 + 3/12
Which expressions have like denominators that could be used as a next step to add the two fractions?
Select the two correct answers.
- 5/6 + ¼
- 5/6 + 3/6
- 10/12 + 3/12
- 5/12 + 6/12
- 5/12 + 6/24
- 20/24 + 6/24
5.NF.2 2014 MCAS #9 B
5.NF.2 PARCC Performance Based Assessment #4 D, A
5.NF.2 PARCC End of Year Assessment #9 D
5.NF.2 PARCC End of Year Assessment #16 D, C