Overruled! Guide and Answer Key for Instructorsaces.nmsu.edu/matrix/pdfs/overruled_instructors.pdf · Guide and Answer Key for Instructors ... you suggest other ways to solve the

Ask Students to Complete Learner Guide:Distribute the student Learner Guide and ask students to complete the activities. You may wish to have students work in pairs or in small groups.

After students have completed the activities, review the questions and answers with them. Ask:

How did you arrive at your answers? •Can you think of other ways to arrive at the same answer?•

If answers are incorrect, are the mistakes due to computational errors or do students not yet understand the concept? Guide students through the problems again or ask a student who has grasped the concept to lead the review.

Matrix Overruled! Guide and Answer Key for Instructors http://www.matrixlearing.org

View and Discuss Video with Your Students: With your students, watch the 6-minute video, Overruled! at http://matrixlearning.org and spend about 10 minutes discussing the big ideas or key points in the video Ask:

What do you think the video is about? •What did you • learn from it? What tool did the characters in the video use to explain and •solve their problem (graph)? Why was this tool useful? Can you suggest other ways to solve the problem?Can you think of other situations in which proportions might be •used to convert measurements or solve measurement problems (e.g., cooking, distance, or money exchanges)?

1. In the fictional kingdoms of Kingopolis and Queentopia, engineers had to convert King’s feet to Queen’s feet, and vice versa, to build a bridge between the two countries. They had to know that 2 Queen’s feet = 3 King’s feet. Fill in the chart and graph so that people in the two kingdoms can easily convert one form of measurement to the other.

A. B.

Overruled! WorksheetWatch the video Overruled! at http://matrixlearning.org and complete these activities.

An instructor guide is available at the Matrix Learning Web site.

Matrix Bad Date Student Worksheet http://www.matrixlearing.org

Queen’s Feet King’s Feet1

2 3

3

4 6

5

10

King’s Feet Queen’s Feet1

2

3 2

4

5

10

Learning Processes:Text comprehension.•

Mathematical reasoning.•

Skill development and attainment.•

Problem solving.•

Goals/Standards: The Overruled! video is about ratios and proportions and, more specifically,aboutconvertingmeasurementsusingratiosandproportions. Watching the video and completing the activities in the learner guide will help students learn that:

Variousmathematicaltechniquesarehelpfulinfinding•the missing part of a proportion, including tables, graphs, measurement and equations.

Graphing proportions on a coordinate plane results in a graph •that is linear.

Proportions are multiplicative situations. •

Given an application problem, using the units can help to set up •the correct proportion.

Different characteristics are always, sometimes or never present •in a rate, unit rate, ratio and proportion.

Overruled! Guide and Answer Key for Instructors


Matrix Overruled! Guide and Answer Key for Instructors http://www.matrixlearing.org 2

Bonus Activities – Select one or more of these to do with your students after the Learner Guide.

Everyone is happy that the bridge will be built. However, the hot dog vendor is frustrated that the 1. hot dogs are 1 King’s foot long, while the buns are 1 Queen’s foot long. Ask students to draw a picture of one of the hot dogs.

(Note: Students should draw a picture of hot dog and bun.)

Ask students to imagine that hands instead of feet were used as measurements in the two countries, 2. and a King’s hand is 2 ½ times as long as a Queen’s hand. Ask them to make graphs or charts so that the citizens can easily make the conversion from King’s hands to Queen’s hands.

(Note: Students should understand that 2 ½ x 1 can be written as a ratio [2 ½:1]).

Ask students to assume roles of various citizen-workers in either Queentopia or Kingopolis. Ask 3. them to think of a measurement problem that came up during the course of work and write a story about it and how they solved it.

(Note:Forexample,atilerlayingtileintheQueen’sroyalhallfindsthatshehastakenthefloorareameasurementinQueen’sfeet,butthetilesarecomingfromKingopolisandtheyaremeasured in King’s feet. Did she order too many or too few tiles and how does she solve the problem?)



Instructor’s Answer Key

1.InthefictionalkingdomsofKingopolisandQueentopia,engineershadtoconvertKing’sfeettoQueen’s feet, and vice versa, to build a bridge between the two countries. They had to know that 2 Queen’s feet = 3 King’s feet. Fill in the chart and graph so that people in the two kingdoms can easily convert one form of measurement to the other.

A. B.Queen’s Feet

King’s Feet

1 1 1/2

2 3

3 4 1/2

4 6

5 7 1/2

10 15

King’s Feet

Queen’s Feet

1 2/3

2 1 1/3

3 2

4 2 2/3

5 3 1/3

10 6 2/3

Instructors: Ratios on a graph should always yield a straight line. If your student’s line is not straight, help them see a point that doesn’t fit, and question if it is correct.



3. The Queen decided that she wanted a new royal purple banner to flyoverthenewbridge.Thebannerwillrequire6Queen’sfeetofpurple silk fabric. By looking at the chart to the right, can you tell how many Duke’s feet of silk will be needed for the banner?

6 Queen’s feet = ______ Duke’s feet

2.The Duke of Good Arches has very large feet. They are 1 1/2 times the size of the Queen’s feet or, it takes 1 1/2 Queen’s feet to equal one Duke’s foot. Using the table below, make a graph that compares Duke’s to Queen’s feet. Remember that points plotted on the graph will make a straight line.

Queen’s Feet

Duke’s Feet

1.5 1

3 2

4.5 3

9 6

12 8



6. Joe from New York marries Maria from Italy. After the wedding in Milan, the couple starts to drive to Venice for their honeymoon. After driving for a little while, Joe sees a road sign that says, “Venice -- 200 km.” Joe is used to thinking about distance in miles, and he wonders just how far away Venice is in miles. Luckily, Maria has made a table for him so that he can convert the metric distances into miles.

A.Mariasays,“We’llstopforlunchinabout40kilometers.”Usetheconversiontabletofindoutfor Joe how many miles that is. 24.85 miles

B.JoeknowsthatwhenhedrivesintheUnitedStates,hehastofillupthegastankaboutevery250 miles. Maria looks at the conversion chart. Is it more like

300 kilometers

X 400 kilometers

500 kilometersKM Miles

1 .62

10 6.21

20 12.43

30 18.64

40 24.85

50 31.07

100 62.14

150 93.21

200 124.27

Instructor:Help your students estimate the answer to this question. For example, ask them where 200, 300 and 400 kilo-meters would fall on the chart, and make comparisons. Also, they may notice that 250 miles is approximately twice 124.27 and 400 kilometers is 2x 200.



A. Can you make a table so that Joe can convert his recipe?

B.Nowhelphimfigureouthowmanytablespoonsofingredients he needs to make the cake.

7. Joe and Maria are back from their honeymoon. Joe wants to impress Maria by baking a cake. They haven’tfinishedunpackingandJoecanonlyfindthemeasuringspoonsandnotthemeasuringcups!He knows that 1/4 cup is equal to 4 tablespoons.

Cups Tablespoons

1/4 4

1/2 8

3/4 12

1 16

Joe’s Recipe

1/4 cup = 4 tbsp

1 cup of butter 16 Tbsp butter

1 1/2 cups sugar 24 Tbsp sugar

2 1/2 cups of flour 40 Tbsp flour

1/2 cup cocoa

8 Tbsp cocoa

6 eggs

©2007 NMSU Board of Regents in collaboration with the Ohio Board of Regents. All rights reserved. Matrix products were developed under a cooperative agreement from the U.S. Department of Education, PR/Award Number U295A050004. However, contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government.

Documents

Overruled! Guide and Answer Key for Instructorsaces.nmsu.edu/matrix/pdfs/overruled_instructors.pdf · Guide and Answer Key for Instructors ... you suggest other ways to solve the