Race for Equivalency!
An Equivalence Relay Race
Targeted grade level: 5th graders
Brief overview: Race for equivalency! Students compete in a fractions based relay race, where they work in their teams to discover fractional equivalencies for common decimals and percentages.
Goals:
* Students will understand the mathematical term equivalency
* Students will practice adding fractions
* Students will equate fractional equivalencies from decimal and percentages (for this specific version, ranging from .25 to 2.50)
* Students will manipulate fractions to form decimals and percentages (for this specific version, 1/4, 1/2, 3/4, 2/5, and 3/5)
* Students will cooperate in small groups to solve problems
* Students will discuss group strategies with each other
* Students will use mental mathematics to solve equations
* Students will reflect upon strategies used to complete this activity in their math journal
Materials:
* Colored number tags (directions included)
* Problem cards (directions included)
* Table
* Whistle
* Bell or buzzer
* Watch
* Small box per team
* Marker for starting line
* Area appropriate for a relay race
* Assessment sheet (directions included)
* Each students should bring their math journal and writing instrument
* Math manipulatives class is familiar with using
* "After the Race" discussion questions (included)
* "For Reflection" directions (included)
* Possible Answers sheet (directions included)
To Do Before Class:
* Decide how many teams of 5-6 you will need for your group of students
* Construct number tags.
* Construct sets of identical number tags of fractions on different colored backgrounds for each tem, enough for each student to have one (for this version, I chose 1/2, 1/4, 3/4, 2/5, and 3/5) Each team should have the same fractions to work with. (See "Number Card" directions)
* Construct sets of problem cards that feature decimals and percentages that can be made from the fraction number tags for each team (for this version, I chose decimals between .25 and 2.5, and percentages between 25% and 250%) Each team should have the same problems to work with. (See "Problem Cards" directions)
* Create a "Possible Answers" sheet
* Set up an area to have a relay race, including a clearly marked starting line. Keep in mind that participants will run the length at least twice per every problem you set up.
* Have teams run from starting line to a table where a small box is set up for each team. The box will hold the problems they need to solve.
* Have a buzzer or bell for the winning team to ring, and a whistle to start off the race.
Number Cards:
You are making number name tags, similar to the ones used in marathons. Gather colored paper, card stock, or poster board - six pieces of the same color for each team. Choose 5-6 basic fractions that students have been working with, or need help manipulating. Write fractions in large, dark numbers on the colored paper. You want one each of each color. Laminate cards. Punch two holes near the top left and right hand corners. Place a safety pin through each hole.
Problem Cards:
Using the 5-6 basic fractions you choose to put on the number cards, choose decimal equivalencies that are represented by the fractions. Combine these to create problems that require sub-groups of the fractions. Order them , so that the problems get progressively harder, and build on the skills they are using. On index cards, number the back, in small writing in a corner, A-F the number of teams you have, and 1-20 the number of problems you want students to work through. Flip them over, and, going down your list, write either the decimal or percentage on the index cards. I alternated percentages and decimals among the teams, so that team A had 50% and team B had .50 for card #2. Make sure each team has the problems in the same order, so that they are working progressively through the problems. When finished, place each teams cards face up in a small box. If the cards are knocked over, use coding on the back to reorder them.
Possible Solutions Sheet:
After creating the problems you want students to solve, go through and write down all the possible combinations for each answer next to the problem on your own "cheat sheet". This will keep you from having to solve fraction addition problems as the teams rush forward to get their next card.
Game directions:
This is a relay race. Everyone will have a fraction that they play in the game. The purpose of the game is to be the first team to work through the stack of problems using the fractions on your team.
When the race starts, the first person in line runs to the table, picks up the top card, and races back to the team. As a group, figure out what fraction(s) that you have are equivalent to the decimal or percentage on the card. The person(s) whose fractions are equivalent to the number on the card race up to the table. There will be a monitor at the table. If the fractions that come to the table do not equate the number on the card, the monitor will ask you to go back to your team and try again. If the fractions are equivalent to the number on the card, place the old card next to the box, pick up the next card in the box, and race back to the team.
After a set period of time, the monitor will blow the whistle. Which ever team solved the most amount of problems are the victors. If you solve all of the problems in your team box before the whistle, race up to the table and [ring the bell, buzz the buzzer] to let everyone know you have finished.
In Class Activity:
* Ask students to bring their math journals, writing instruments, and any other math manipulatives for working with fractions
* Ask students what "equivalency" means. Lead mini-review on how fractions, decimals, and percentages related to each other in terms of equivalency.
* Go over game directions, including how much time the race will last
* Break into teams of 5-6
* Hand out number tags, and ask students to pin them to the front of their shirt
* Ask teams to sort themselves in numerical order, from largest to smallest
* Have teams line up relay style, from largest to smallest fraction, at the starting line
* Begin race
* As teams run up to get their next card, check to make sure the fractions on their shirts are equivalent to the number on their card. If they are not, ask them to go back to their team and try again.
* After the set amount of time, blow the whistle to signal the end of the race.
* Have teams come up and engage in a group discuss using "After the Race" questions (included)
* Hand out "For Reflection" questions (or post on white board)
* Ask students to reflect on this activity in their math journal
Possible Follow-Up Activities:
* This race can be used to introduce the idea of equivalencies in an algebraic sense. Some students may write their reflections using algebraic ideas. Read their reflections to assess their readiness for pre-algebraic concepts of balancing an equation.
* This race can be easily modified to work with different aspects of mathematics
* Ask students to design their own math relay race, and give them time to teach it to the class
* Ask students to design a math game for younger students. Give them time to teach it to a group from a primary class.
After Race discussion ideas:
* Why do you think this game is called Race for Equivalency?
* How well did your group work together?
* What's one thing that went well?
* What's one thing you would do differently if you played this game again?
* What strategies did your team devise to solve these problems?
* Which ones were the most accurate?
* Which ones were the fastest?
* What manipulative did you use? (Mental math, paper and pen, talking it out, calculators, Cruisenaire rods, and so on)
* Which ones were most accurate?
* Which ones were fastest?
* What are some examples of when you have needed to know fractional equivalencies?
* Who do you think uses fractional equivalencies at their job?
For Reflection ideas:
Please reflect on your experiences while playing Race for Equivalency. Include:
* What does equivalency mean
* Two strategies your group tried
* Two other strategies you would try in the future
* What are other examples of using equivalencies at school?
* What are some examples of using equivalencies outside of school?
* How did your team deal with times when different people saw different answers?
* Explain in English how you solved three different problems.
* Explain using math symbols how you solved three problems.
* What's one thing that went well?
* What's one thing you would do differently if you played this game again?
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