1 Engagement in the Mathematics class Marlene Wilks, Presenter

2 Engagement in the Mathematics class Activity 1: Read the article “10 BIG MATH IDEAS” by your self (15 minutes) Use the “Stop and Jot” Sheet to record “Glaring Headlights”. Working with at least one other person, read again the #ed paragraph assigned to you. List 5 outstanding ideas to share with the group. Glaring Headlights are points that jump out at you!

3 Goal: Students understand the concept of ratio when comparing part to whole Objectives: Given a problem set, students are able to determine exact amounts using ratios to compare. Objectives: Given a problem set, students are able to determine exact amounts using ratios to compare. Students are able to represent ratio in three different forms. Students are able to represent ratio in three different forms. Students discuss and write their solution process. Students discuss and write their solution process.

4 PRE-ASSESSMENT Write an equivalent ratio for 4:16 Write an equivalent ratio for 4:16 What is the quotient of ¼? What is the quotient of ¼? 1:4 can be written as ¼. One-fourth also represents one out of four parts. Is there a difference between ¼ as a ratio and ¼ as a fraction? 1:4 can be written as ¼. One-fourth also represents one out of four parts. Is there a difference between ¼ as a ratio and ¼ as a fraction?

5 SAMPLE ENGAGEMENT LESSON Ratio Problem: Mini-Lesson: Problem Set: There are 20 students in Mr. Wyatt’s class. Three out of 5 students are girls. How many students are girls? Note: As the mini-lesson progresses, examine your notes to see if any idea suggested in the article has been confirmed.

6 Model Lesson What do I know = What do I know =Paraphrase: -20 students in all -For every 5 students, 3 are girls. 3/5 or 3:5 or 3 divided by 5. 3/5 or 3:5 or 3 divided by 5. I can use 20 objects to represent the 20 students. students. I will make 4 groups of 5 since there are 20 in all I will label 3 out of every 5 objects girls Then I will count the total labeled girls.

7 Alternative What is another way that I can solve the problem? What is another way that I can solve the problem? If 3/5 = 6/10 = 12/20 I am thinking that when I have 5, I take out 3 for girls, so if I have twice 5 then I would take out twice 3 = 6/10. If I then have twice 10, then I would take out twice 6 = 12/20.

8 Trial Run Draw a diagram to represent the solution to the problem set below: Imagine there are 28 tiles on your desk. If 4 out of every 7 tiles are black, how many are black? (3 minutes) You have 3 minutes to work with your partner. (Share out)! Look for responses and confirmations using classroom language—I agree... I disagree... I disagree... I do not think... I do not think... I think... I think...

9 Independent Group Work Janice has a bag of marbles that she decided to share among three friends. For every marble she gives Frank, she gives Dwayne 2 marbles, and for every 2 marbles she gives Dwayne, she gives Juney 3 marbles. If it took her 5 turns to distribute all the marbles, how many marbles does she have altogether? Janice has a bag of marbles that she decided to share among three friends. For every marble she gives Frank, she gives Dwayne 2 marbles, and for every 2 marbles she gives Dwayne, she gives Juney 3 marbles. If it took her 5 turns to distribute all the marbles, how many marbles does she have altogether? Describe the solution process. Describe the solution process.

10 Directions for Independent work Working with a partner, select one of the problems and spend the next 10 minutes discussing and then writing your solution. Working with a partner, select one of the problems and spend the next 10 minutes discussing and then writing your solution. Be prepared to share out today! Be prepared to share out today!

11 Independent Group Work For every 8 spelling tests Justine took, she earned 3 perfect scores. If Justine earned 12 perfect scores this year, how many spelling tests did she take? For every 8 spelling tests Justine took, she earned 3 perfect scores. If Justine earned 12 perfect scores this year, how many spelling tests did she take? (Describe your solution process) (Describe your solution process)

12 Independent Group Work Place 30 tiles on your desk so that 4 out of 5 tiles are white and the rest are shaded. How many tiles are white? How many are shaded? Place 30 tiles on your desk so that 4 out of 5 tiles are white and the rest are shaded. How many tiles are white? How many are shaded? (Describe your solution process). (Describe your solution process).

13 Independent Group Work Sue reads 2 books for every 4 books that Georgine reads. When Georgine completes her 24 th book, how many books would Sue have completed if they continue to read at the same rate? Sue reads 2 books for every 4 books that Georgine reads. When Georgine completes her 24 th book, how many books would Sue have completed if they continue to read at the same rate? Share in writing with your audience how you solved the problem. Share in writing with your audience how you solved the problem.

14 Challenger 3/5 = ?/20 3/5 = ?/20 Explain why the equation above represent the problem in the mini-lesson and share in writing how you would find the value of the ? using number sense strategies.

15 Independent Work Students are working in small groups. Students are working in small groups. Teacher circulates to ensure that students are working. Teacher circulates to ensure that students are working. Teacher pulls small group for guided math lesson. Teacher pulls small group for guided math lesson. Groups of students put their solution on a chart paper. Groups of students put their solution on a chart paper. Students display solution and share out. Students display solution and share out. Class asks questions. Class asks questions.

16 POST-ASSESSMENT The ratio of shirts to the ratio of pants that Ronnie has is 4:6. If you counted all of Ronnie’s shirt and pants, which of the choices below could not represent the total number? The ratio of shirts to the ratio of pants that Ronnie has is 4:6. If you counted all of Ronnie’s shirt and pants, which of the choices below could not represent the total number? 1. a. 10 b. 15 c. 20 d State your reasons for the decision you make. The perimeter of a triangle is 60 cm. If the sides are in the ratio 3:4:5, find the length of each side of the triangle. The perimeter of a triangle is 60 cm. If the sides are in the ratio 3:4:5, find the length of each side of the triangle.