Multiple Means for Engagement Key Questions Formative Assessment Summary This task allows for activity participation as they explore the meaning of ratio and rate. It allows time for evaluation of their work. Ratio/Rate Cards Sort – Put students in groups of two or three. Ask students to sort cards (Attachment #1) into categories (do not give them any guidance, such as titles, amount of categories, etc.) (SMP#1) Have students explain their categorization. Is there evidence of knowledge of part-part, part-whole, and “other”? (SMP#3) Discuss this chart: Reference: Adapted from Van de Walle, Teaching Student Centered Mathematics, grades 5-8, volume 3, pg. 155 Ask: Would you change the arrangement of your card sort given this new information? Why or why not? What do you notice about the rate cards? Possible answer: They use different types of measures. What other real life examples of rates can you give? (SMP#6) Invite student volunteers to explain the definition of unit rate, and guide student responses into a broader discussion: The students can construct viable arguments and critique the reasoning of others by justifying conclusions as they sort the cards. (SMP# 3) Attend to precision is done in this activity as the students communicate with others and try to use clear mathematical language when discussing their reasoning. . (SMP#6)
A unit rate represents a rate with a denominator of 1 in fraction form. Rates are usually expressed in per unit form. Examples include: miles per hour, pizza slices per person, inches per foot, heartbeats per minute, cost per pound, etc. Return to the card sort. Which rate cards are rates and which are unit rates? Review your original sticky notes and classify (or re-classify, if necessary) students’ authentic life examples. (SMPs #1, #3, #6) Activity 2 UDL Components Multiple Means of Representation Multiple Means for Action and Expression Multiple Means for Engagement Key Questions Formative Assessment Summary UDL Components: Principle I: Representation is present in the activity. Students will use this activity as an opportunity to access prior skill from earlier grades and practice with a new idea for finding unit rates. Principle II: Expression is present in the activity. The gallery walk allows students movement as they solve the problems around the room. Principle III: Engagement is present in the activity The gallery walk fosters discussion, collaboration and community in order to compare their prices. Finding the unit rate using equivalent ratios. Show two examples: Example #1: 15 hamburgers for $75. How much per hamburger? (Note to teacher: Make sure students are solving using equivalent ratios.) = = Make sense of problems and persevere in solving them on the gallery walk as they monitor their own progress and change their approach if necessary. (SMP#1) The students model with mathematics as they apply the mathematics they know to solve everyday problems. (SMP# 4) The students are attending to precision as they communicate precisely with others on
bouquet 6 to 18 12 to 1 in supply room soccer balls 5 to 8 Number of footballs per class 5 : 5 or 1 : 1 Number of points earned per pupil or Number of points earned to number of possible points Number of points earned to number of points not earned 80 : 20 Probability of getting a head with one coin toss Probability of getting a head with one coin toss 1 to 2 Number of heads in 10 tosses 6 to 10 Number of green M&Ms to total candies in bag Number of miles per gallon Cost of cereal per ounce Number of heart beats per minute 67 : 1 Number of pizza slices per person 3 : 1 Number of boys to number of girls in same class 11 to 13 Number of girls to total number students in class 13 : 24 Cost of bananas per pound $1.20 : 1 Number of apples to number of oranges 5 : 7 Number of blue socks to total number of socks in the drawer 6 to 14 Number of miles per hour 67 : 1 Number of gallons in 4 minutes 12 : 4 Number of songs to cost of songs 20 : $5.00 Attachment #2: Ratio/Rate Card Sort - Answer Sheet Number of red roses to number of flowers in bouquet Number of red roses to number of yellow roses 6 to 18 Number of roses per bouquet 12 to 1 Number of baseballs to number of bats in supply room Number of footballs to number of soccer balls 5 to 8