Teaching Priority Concepts
in Math: Grade 8
Tricia Profic
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
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?”
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?
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
Wore
goggles
20
34
14
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?
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?
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.
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?
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?
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?
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?
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….
Activity
 Draw on paper any shape you would like
and a vector 𝐴𝐵
 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
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
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
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
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
Sequencing Rigid Motions
Congruence of Figures using
Rigid motions
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.
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