Teaching Priority Concepts in Math: Grade 8

1. Teaching Priority Concepts in Math: Grade 8 Tricia Profic

2. State Updates • Module 1 and Module 2 are available on engage for grade 8 • Module 1 Link • Module 2 Link • The first quarter to half of the year’s modules are “supposed” to be available at the end of the month • Annotated sample questions from April’s state assessment are posted on engage as well • Sample Questions link

3. Tape Diagrams • Promote perseverance in reasoning through problems. • Develop students’ independence in asking themselves: • “Can I draw something?” • “What can I label?” • “What do I see?” • “What can I learn from my drawing?”

4. Opening Exercise: 88 children were in swimming camp. One-third of the boys and three-sevenths of the girls wore goggles. If 34 students wore goggles, how many girls wore goggles?

5. 88 children were in swimming camp. One-third of the boys and three-sevenths of the girls wore goggles. If 34 students wore goggles, how many girls wore goggles? 88 Children at swim camp Boys Girls 34 54 Did not wear goggles Wore goggles 20 Wore goggles 14 34

6. Try to use tape diagrams to answer the following question: 94 children are in a reading club. One-third of the boys and three-sevenths of the girls prefer fiction. If 36 students prefer fiction, how many girls prefer fiction?

7. 94 children are in a reading club. One-third of the boys and three-sevenths of the girls prefer fiction. If 36 students prefer fiction, how many girls prefer fiction?

8. Let’s practice with tape diagrams Two pears and a pineapple cost $2. Two pears and three pineapples cost $4.50. Find the cost of a pineapple.

9. Example 2 Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and 1/2 of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether?

10. Example 3 Sana and Amy collect bottle caps. The ratio of the number of bottle caps Sana has to the number Amy has is 2:3. The ratio became 5:6 when Sana added 8 more bottle caps to her collection. How many bottle caps does Amy have?

11. Example 4 The ratio of songs on Jessa’s phone to songs on Tessie’s phone is 2 to 3. Tessie deletes half of her songs and now has 60 fewer songs than Jessa. How many songs does Jessa have?

12. Congruence and Rigid Motions • How do you define congruence? • Why are we defining congruence in terms of rigid motions? • To avoid having to directly measure objects: Can we really measure with accuracy? • Are opposite sides of a rectangle really congruent?

13. Translations • How do you define a translation? • Module definition of a translation: • A basic rigid motion that moves a figure along a given vector. • Yes, vectors in 8th grade….

14. Activity • Draw on paper any shape you would like and a vector • Trace that shape and vector onto your transparency • Slide your transparency moving your point A to end at your point B • visual of a translation

15. Reflections • How do you define a reflection? • Module definition of a reflection: • A basic rigid motion that moves a figure across a line • Also, if you connect any point to its reflected image, the line of reflection bisects that segment

16. Activity • Draw on paper any shape you would like and a line you would like reflect your image on • Trace that shape and line of reflection onto your transparency • Flip your transparency over to see how the image was reflected on the line you chose to draw • visual of a reflection

17. Rotations • How do you define a rotation? • Module definition of a rotation: • A basic rigid motion that moves a figure around a point, d degrees

18. Activity • Draw on paper any shape and a point you would like to rotate your shape around • Trace that shape and point on your transparency • Turn your transparency counter clockwise around the point you drew, keeping your transparency matched up with your point • Visual of a Counterclockwise Rotation

19. Sequencing Rigid Motions

20. Congruence of Figures using Rigid motions

21. Congruence of Angles • How to prove the congruence of angles when you have parallel lines cut by a transversal using rigid motions. • Proving the angle sum of the interior angles of a triangle is 180 degrees given known facts about straight angles and the relationships between angles with parallel lines cut by a transversal.

22. Today’s Task • Each pair will be given a lesson from Grade 8 Module 2 to analyze • We know that some of these lessons will need modifications to reasonably teach these concepts • Please fill out the lesson plan form • If you modify any of the class problem sets or homework assignments, please add them to the lesson plan word document • After building your lessons, we will regroup and modify the mid-module and end-of-module assessments to add multiple choice questions