Unit 3 Equal Partitioning

Unit Driving Question

How is equal partitioning used in our daily lives?

Essential Questions

1. How can we use equal partitioning?

2. How can we use fractions to make a whole?

3. How do we use equal parts of a dollar?

4. What do the partitions tell us about time?

Big Ideas

1. Fractions are numbers that describe parts of a whole.
2. Minutes are parts of a whole hour. 
3. Coins are part of a whole dollar. 

Technology Resources

The following apps, websites, and smartboard lessons can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards.  They are also useful for students who may need reinforcement, remediation, or differentiation.

• Third Grade List- This list has resources that can be used all year long.

Resources Within This Unit

• Big Idea 3:

• Fewest Amount of Coins: This is a teaching tool to help students understand the value of coins and how to find the fewest amount of coins to represent a given value. Use this on a smartboard or students can use their iPads (if district provides) to find the value of coins and exchange coins based on their value. (ex: two dimes and a nickel can be exchanged for a quarter). If you click the hundreds block in the bottom right corner of the screen, students can see how the coins relate to one another based on their value.

Additional Resources

• Fraction Strips- This is a great resource to use when teaching students how to compare fractions.

• Interactive Clock- Clock to use on the board to practice time.

• Tony Fraction- A Pizza Fraction Game for Kids -Students practice creating fraction pizzas based on client orders.

Launch Task

1 Lesson

Renting Mr. Jackson’s Storage Spaces

This task involves equal partitioning with fractions, money, and time. Students are asked to help Mr. Jackson decide if each renter is paying a fair price for their rental space. 

Big Ideas for Development Lessons

3-4 Weeks

Big Idea 1: Fractions are numbers that describe parts of a whole.

Collaborative Engagement 

1. Ants in the Picnic Basket: Students can apply problem-solving strategies to solve the task, such as making diagrams or creating charts.
2. Making and Investigating Fraction Strips: Students make and use a set of fraction strips to represent the length model, discover fraction relationships, and work with equivalent fractions. 

Key Resources 

1. Parts of a Square: Students investigate the ways shapes can be divided into equal pieces with one or two cuts. The lesson provides a review of the following vocabulary terms: square, triangle, and rectangle; congruent, one-half, and one-fourth. The other lessons in this unit build on this introductory lesson.
2. Paper Folding: Give students three pieces of rectangular (or square) pieces of paper. Have students fold each into “halves”. Tell them they all must be different from each other. Have them share what they came up with. Ask them to look at their shape and identify they bigger piece. Some may say they are the same size. Others may say they are different. Prompt students to think of the importance of equal sizes (ex: If this was a candy bar, would it be fair to split it in half with a friend and they get the bigger piece?). Have them continue the investigation with common fractions, such as fourths and eighths. Distribute more sheets of paper for fractions like thirds or sixths.
3. Fractions as Numbers on a Number Line: Students extend and deepen second grade practice with “equal shares”  to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number lines.
4. Representing and Comparing Fractions: On page two, you will find a table of contents that includes links to various fraction concepts.
5. Another Look at Fractions of a Set: This lesson gives students another opportunity to explore fractions using the set model. This lesson is integrated with other areas of the math curriculum including data analysis and statistics.  

Additional Resources 

1. Mega Fun Fractions: Mega-Fun Fractions to provide in one resource a variety of ways for you to immerse your students in fraction concepts. All activities address one or more of the NCTM fraction standards listed above. The range of fraction lessons includes hands-on explorations and activities that invoke problem-solving, reasoning and proving, communicating, connecting, and representing fractions.  

Big Idea Formative Assessment

1. Fraction Test 3rd Grade: This is a short (& free!) formative assessment from Teachers Pay Teachers that you can use at the end of teaching Big Idea 1.
2. Representing Fractions: This is a math probe that assesses students' understanding of equal partitioning.
3. Tamiko's Puzzles Performance Assessment: This is a performance assessment that assesses students' understanding of Big Idea 1. For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module. 

Evidence of Understanding 

• Divide a whole into equal size partitions.

• Discuss and write fractions using appropriate vocabulary and symbols.

• Split number lines into equal sized partitions to better understand the value of the fraction in comparison to the whole.

• Represent fractions in a variety of ways to understand that the value is always the same in comparison to the whole.

• Compose and decompose unit fractions with the understanding that all the partitions are the same size.

• Sequence a set of unit fractions from least to greatest.

Big Idea 2: Minutes are parts of a whole hour.

Collaborative Engagement

1. Party Time: Students will be planning a party for a second-grade class. To start this activity have the students think of activities they would want to do at their own party, and estimate the amount of time it would take for each activity.  To increase engagement have students use Judy clocks. Some students may need calculators. Adapt this activity to fit your classroom needs.
2. “Fractions of Time”This is another idea to engage your students. Using a paper plate, have your students create a clock. Have the students divide the clock into halves, fourths, and twelfths using different colors. Discuss how fractions can be related to time. 

Key Resources 

1. Telling time in 5-minute intervals: Students can read the time on the clock to the nearest 5 minutes.
2. Check The Time: The student will tell and write time to the nearest five minutes, using analog and digital clocks.
3. Telling Time: Students will tell time in quarter-hour intervals using an analog clock. It also includes time on a number line. 
4. Creating a Morning Schedule: Students create a schedule for two different students based on the time they need in the morning. Adapted from North Carolina 3-5 Formative Instructional and Assessment Task

Additional Resources 

1. Exploring Time: This is a resource that includes many activities and ideas on how to teach time. 

Big Idea Formative Assessment 

1. Time Assessment: This is a great assessment to use with students after teaching big idea 2. It includes clocks for students to use to answer questions as well as word problems.
2. Dinosaur Museum Performance Assessment: Assessment also covers 3.N.2.3 and 3.N.2.5. For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module. 

Evidence of Understanding 

Tell time to the nearest five-minutes using analog and digital clocks.

• Identify the minute and hour hand.

• Create clocks that are divided into twelve 5-minute intervals.

• Use multiplicative strategies, such as skip counting and repeated addition, to determine the time and solve time word problems.

Big Idea 3: Coins and Bills are used in Money Transactions.

Collaborative Engagement 

1. Counting Coins: Students will be working in groups or pairs to make a fair share of change. It would be great to provide students with the opportunity to use manipulatives such as play money. When solving for the answer to this problem.

Key Resources 

1. Problem-Solving with Coins and Bills: Beginning with the largest coin value (often the quarter), students count the total value of a group of coins, applying their knowledge of addition strategies (2.NBT.5) and skip-counting by fives and tens when there are multiple nickels or dimes.
2. Computation with Money: This resource provides engaging hands-on lessons and activities that provided students the opportunity to learn about different ways to create change up to a dollar.  
3. It Cost How Much?: This resource includes a lesson, station activity ideas, and various assessments. It also includes extensions and accommodations.
4. Fewest Amount of Coins: This is a teaching tool to help students understand the value of coins and how to find the fewest amount of coins to represent a given value. Use this on a smartboard or students can use their iPads (if district provides) to find the value of coins and exchange coins based on their value. (ex: two dimes and a nickel can be exchanged for a quarter). If you click the hundreds block in the bottom right corner of the screen, students can see how the coins relate to one another based on their value.
5. Coin Sorting Map: This can be used for students to organize the coins they are using. It is also a visual way for them to see how certain combinations have more coins than others.
6. Take it to the Bank: This activity has students use hands-on manipulatives to see how different coin combinations can make the same amount of money. Students learn about “trading” and how a bank works. 

Big Idea Formative Assessment

1. Working with Coins: This formative assessment has students count coins and answer word problems.

Evidence of Understanding

Sort and combine coins, such as pennies, nickels, dimes, quarters, and half dollars, to determine the amount up to one dollar.

• Use strategies such as sorting and skip counting when adding up to a dollar and solving word problems involving money.

Add bills up to $20 using one, five, and ten dollar bills. 

Unit Closure

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

• Renting Mr. Jackson’s Storage Space (part 2) This is the initial task that is revisited to add some rigor at the end of the unit.