Are Fractions Your Arch-Enemy? Kick Mnemonics to the Curb! Stephanie Belotte - Brookville Middle School Daphney Denton - Brookville Middle School

There are many meanings of fractions. Students must experience fractions. Daphney -

Take a few minutes and discuss with your table group how you would go about solving the problem shown. Please jot down your ideas on the dry erase board and be prepared to share with the rest of the group. You do not have to actually solve the problem but may choose to do so if you would like. Would anyone like to share what their team discussed? I know this may drive the teams crazy that went ahead and solved the problem, but we are not going to talk about the solution just yet! Instead, we are going to explore how we can build up to having our students solve a problem with this with confidence. To do that we want to begin exploring pattern blocks.

Pattern Blocks

Region Relationships: Explore how the pattern blocks relate to each other. Daphney - Students begin to build problem solving skills through exploration! Use your pattern blocks to help. How can you lead your students to begin recognizing these triangles as parts of a whole, without telling them?

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Stephanie - Now let’s solve it Stephanie - Now let’s solve it! Use your pattern blocks to help determine the solution to Farmer Fred’s problem. Even if your team solved the problem earlier try it again using the pattern blocks at your table. What did each team come up with? How did you reach your solution? Are there other ways that could have also been used? What would they be? Reference packet - Daphney will explain a whole doesn’t have to be one pattern block. Transition to how many ⅓ make a whole (example). Develop student understanding of relationship between numerator and denominator. Discuss estimating fractions to the nearest ½ or whole number. Is it closer to zero, ½ , or one whole.

Comparing/Ordering Rational Numbers The following chart shows changes in profits for Acme Motors for the months of July, August, September, and October of last year. Mr. Grimes, your boss, wants you to write the increases in order them from largest to smallest. 3/8 3/5 5/6 1/3 July Aug. Sept. Oct. Daphney - What will students need to know and understand before solving this problem? What kind of activities would help students build the skills needed? What vocabulary do students need to begin building and using? Participants put responses on poster paper. (one question per poster/different marker per team) Vocabulary: numerator, denominator, zero fraction,unit fraction, proper fractions, improper fractions, mixed numbers, etc.

Fraction Strips

Naming Fractions As students connect the area model (fraction strips) with the number line model, their understanding of fractions is increased. After students explore how many strips of each size are needed to make a whole, transition to the number line by asking, “What do we need to know on the number line?” As they recognize where 0, 1, 2, etc. are located, ask them to find ½. Stephanie - While pattern blocks help students develop a conceptual understanding of fractions there are also many other effective tools that can aid in such a development, including fraction strips. Fraction strips help students to visualize various fractions, compare fractional parts to a whole, as well as explore equivalent fractions. While we are going to explore fraction strips together in the next few slides, there are several grade specific fraction strip activities in your folder. You can find the activities on the yellow paper.

Use Fraction Strips to Help you Solve the Following: Al, Bill, Carrie, Danielle, Enrique, and Fabio are each given a portion of the school garden for spring planting. Here are the portions: Al = 1/4 Bill = 3/16 Carrie = 1/8 Danielle = 1/16 Enrique = 1/4 Fabio = 1/8 If Carrie, Fabio, and Al decide to partner up and share the work what portion of the garden will they have control over? Stephanie - Use the fractions strips at your table to model your thinking as you solve the problem. Ask a volunteer to come up and model what they did using the magnetic fraction strips. Share differences in how each group may have solved the problem.

Comparing/Ordering Rational Numbers The following chart shows changes in profits for Acme Motors for the months of July, August, September, and October of last year. Mr. Grimes, your boss, wants you to write the increases and decreases as rational numbers and order them from largest to smallest. 3/8 3/5 5/6 1/3 July Aug. Sept. Oct. Daphney - Now that we have worked with unit fractions, let try a more challenging problem. Again, use the manipulatives to model your thinking while solving the problem. Ask for a different volunteer to come demonstrate how they solved it.

Now let’s take a look at how we can represent fractions on a number line to establish number sense of fractions.

Building Number Sense of Fractions Daphney - After watching this video, did you recognize any vocabulary that was used in your gallery walk? Did you hear any vocabulary that you did not initially think of using? Take a moment and discuss this with your team and have a team member add to the poster paper if needed.

Solve the problem using the number line below. Alex did part of his homework before dinner. He did 2/6 of his homework after dinner. He has 1/6 of his homework left to do. What fraction of his homework did Alex do before dinner? Write your answer in simplest form. Stephanie - Use the number line at your table as you solve the question. Once you are finished, have one team member demonstrate your group’s thinking using a dry erase board at your table. How does using a number line relate to the fractions strips?

Understanding Fraction Equivalents on a Number Line Ryan has 1/4 of a meter of rope and his brother has 5/8 of a meter of rope. They need 1 meter of rope to make a leash for their puppy. Will they have enough rope? Daphney - Now, let’s take it up a notch. Given a number line without the fractions already represented, how would solve the problem? How can the ground work with fraction strips help students gain an understanding of how to label fraction on a number line?

Mary: 3/4 Harry: 1/2 Larry: 5/6 Han: 5/8 Miguel: 5/9 Angela 1/3 Who is Winning? The friends below are playing the game red light- green light. Who is winning? The fractions tell how much of the distance they have already moved. Can you place these friends on a number line to show where they are between start and finish? Mary: 3/4 Harry: 1/2 Larry: 5/6 Han: 5/8 Miguel: 5/9 Angela 1/3 1 Stephanie - Skip for now. Come back to this if there is time.

Jumps on the Ruler See if you can use a ruler to model the following problems: 1 and 1/8 + 1 and 1/2 2 and 1/2 - 1 and 1/4 Stephanie - Using rulers as a tool for modeling fractions and fractional operations helps further develop conceptual understanding rather than teaching students to rely on common denominators or algorithms. Let’s see how your team would approach the following problems using a ruler. How do you think that using a ruler could assist you in teaching fractions within your classroom? Those are all excellent ideas...let’s see if this next video can give you any additional ideas.

Representing Mixed Numbers on a Number Line Stephanie -

Understanding Mixed Numbers on a Number Line Hannah has 2 pieces of ribbon. The first piece is 1 1/2 feet long and the second piece is 2 3/8 feet long. How much ribbon does she have altogether? Daphney - Use the number line sheets in your folder to solve the problem.

Trail Mix Performance Task Congratulations! Because your class was the quietest class at lunch this week, your class has been chosen to help Barbara, the cafeteria manager, make snack mix. For this honor, each student will be allowed to make one cup of snack mix to eat. You may select from these ingredients: coconut, raisins, marshmallows, chocolate chips, cereal, and peanuts. 1 . Choose 3 ingredients from the above list. Write a recipe for 1 cup of snack mix you would like for yourself. Use fractions, but do not use equal amounts of any ingredients. 2. Write a recipe for a class of 24 students, using all ingredients, but different amounts of each ingredient. Only 1 ingredient may be a whole number. Stephanie - How would you see this being used in your classroom?

Resources Region Relationships Pattern Block Lessons Grades 3-5 Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense Daphney - You will find the activities we have used along with addition resource here. We will be sharing this presentation with you by e-mail.