5th Grade Unit 3: Decimal and Fraction Operations

Unit Driving Question

How do we add and subtract with decimals and fractions in real world situations?

Essential Questions 

1. How can estimation help determine reasonableness?

2. What is the relationship of decimal and digits when adding and subtracting?

3. How are decimals related to money in the real world?

4. How does understanding fractions on a number line help with determining the reasonableness of an answer?

5. What are some strategies that enable us to use fractions to solve real world problems?

Big Ideas 

1. The same reasoning for calculating with whole numbers applies to decimals since they are an extension of the base 10 number system.
2. Adding and subtracting fractions require same size parts. 

Technology Resources

       These websites could be helpful online components in your teaching of each Framework Unit

Launch Task

• Karen's Garden - Engaging activity that allows students to connect with their understanding of adding and subtracting decimal amounts using manipulatives, such as base 10 blocks.

Big Ideas for Development Lessons

5 Weeks (approximately 2-3 weeks per big idea) 

Big Idea 1: The same reasoning for calculating with whole numbers applies to decimals since they are an extension of the base 10 number system.

OAS-M: 5.N.3.1, 5.N.3.2, 5.N.3.3

 Collaborative Engagement

How Much Money Are the Coins Worth?- 3 ACT lesson that uses a CoinStar machine video to encourage the students to think about money and values.  They are challenged to determine the total amount and are only given the type of coin and number present.  This really engages their thinking, and also allows the teacher to cue into any misconceptions their students may have about how to add money (decimals).  

Key Resources

1. Entire decimal/fraction unit from Georgia state standards- This is a link to an entire unit on decimals/fractions from Georgia standards.  For this unit, the recommended activities on page 16 of the document are as follows:  It All Adds Up, Rolling Around with Decimals, The Right Cut, and Competitive Eating Records.
2. Summer Olympics- Based on 400m Olympic race results, students will use subtracting decimals to solve problems. 
3. Lessons on Adding and Subtracting Decimals- From Engage NY.  Use pages 130-144, Lesson 9 and 10.  You can use 100 grids or place value blocks to model the problems in written form.  

Big Idea Formative Assessment

1. 10 quick assessments - from HCPSS, go to the Quarter One tasks to access 10 quick formative assessments on adding and subtracting decimals through the thousandths.

Evidence of Understanding

• Understand and apply knowledge of place value patterns to estimate addends/subtrahends

• Understand and apply various estimation strategies such as compensation, front end, or adjustment to determine whether an answer is reasonable

• Demonstrate understanding of addition and subtraction of decimals using visuals

• Apply different strategies to solve real world decimal problems, such as money, metric measurement, perimeter, and analysis of data.

Big Idea 2: Adding and subtracting fractions requires same size parts

OAS-M: 5.N.3.1, 5.N.3.2, 5.N.3.3

Collaborative Engagement

What Should the Freeway Sign Show? - 3 ACT lesson that encourages creative thinking in estimating benchmark fractions to represent distance.  It incorporates measurement of inches and/or cm as well.  The collaboration and justification of answers should lead to rich discourse and communication of ideas.

How Far Apart are the Freeway Exits? - 3 ACT lesson that has students try to figure out the difference between exits with different denominators.  They must think creatively to  determine the correct amount.  It is recommended to even have students use fraction pieces or draw models to help them “see” the problem.

Key Resources

1. Illustrating addition of fractions- From Engage NY, students will use models to add fractions with unlike units using the strategy of creating equivalent fractions.
2. Illustrating subtraction of fractions- From Engage NY, students will use models to add fractions with unlike units using the strategy of creating equivalent fractions.
3. 8 tasks adding/subtracting fractions- 8 quick tasks on adding and subtracting fractions from North Carolina Public Schools
4. Cindy's Cats -This task challenges a student to use knowledge of fractions to solve one- and multi-step problems with fractions.
5. Stuffed with Pizza - Students use fractional parts of a whole, addition and subtraction of fractions, and comparison, to determine if two boys eat the same amount or a different amount of pizza pieces.
6. John's Trip to Disneyland - Students will help John with his trip to by adding and subtracting fractions less than one and use models to help them.  

Big Idea Formative Assessment

Probe Estimating Fractions- A probe from OKMAP that quickly assesses a student’s ability to estimate sums of fractions

Assessment - Formative assessment on adding and subtracting fractions and mixed numbers.

Evidence of Understanding 

• Understand and apply estimation strategies for fractions

• Apply knowledge of benchmark fractions to help estimate for reasonableness

• Demonstrate knowledge of adding like and unlike fraction pieces and mixed numbers using visuals and manipulatives

• Construct visual examples of adding like and unlike denominators and mixed numbers

• Apply procedures to add and subtract  like denominators and mixed numbers

• Apply knowledge of benchmark denominators and equivalencies to add and subtract unlike denominators and mixed numbers

• Make use of various strategies to solve problems using standard length measurement, standard capacity measurement, perimeter, and range of data sets.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)

Re-engagement

1. Recipe- students will create their own recipe for a snack mix for a field day treat using fractions