Unit 7 Shapes On The Coordinate Grid — Unit Plan

TitleAssessment
Lesson 1
Explore the Coordinate Grid
The Last Two Shapes

Elena and Lin were playing a round of Which One? These are the last two shapes. What question can Elena ask to determine which shape is the one that Lin picked?

Rectangle, plotted on coordinate grid. vertices at 1 comma 5, 1 comma 8, 9 comma 5, 9 comma 8. 

Rectangle, plotted on coordinate grid. vertices at 2 comma 5, 2 comma 8, 10 comma 5, 10 comma 8. 

Show Solution
Sample responses:
  • Is one of the sides of the rectangle on the grid line labeled with a 1?
  • Is one of the sides on the grid line labeled with a 10?
Lesson 2
Points on the Coordinate Grid
Coordinates

  1. What are the coordinates of point R?

    0\phantom{0}

    Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. point plotted at 7 comma 3. Labeled R.
    \documentclass{IM} \usepackage{Tikz-IM} \begin{document} \begin{tikzpicture} \begin{axis}[     FirstQuadES,     axis line style={-},     xmin=0,     xmax=10,     ymin=0,     ymax=10,     clip=true,  xlabel={},  ylabel={},  xtick={0,1,...,10},  ytick={0,1,...,10},    xticklabels={,1,...,10},    yticklabels={,1,...,10},     grid=both, ] \node[bigvertex,label=45:{$R$}] at (7,3) {}; \end{axis} \end{tikzpicture} \end{document}

    0\phantom{0}

  2. Plot point T at (3,7).
Show Solution
  1. (7,3)(7, 3)
  2. coordinate grid
Lesson 3
Plot More Points
Missing Coordinate

Here is a coordinate grid with some points labeled.

horizontal and vertical axes, each 0 to 10. 2 points plotted, 0 comma 1 and 6 comma 0. 

Plot and label the points (3,0)(3,0), (0,2)(0,2) and (3,2)(3,2). Explain or show your reasoning.

Show Solution
Sample responses: For 3,0 I took half the distance to 6,0 and for 0,2 I took twice the distance to 0,1. Then 3,2 has a horizontal coordinate 3 and a vertical coordinate 2. 
horizontal and vertical axes
Section A Check
Section A Checkpoint
Problem 1
  1. Write the coordinates for each point on the grid.

  2. Locate the point (3, 0) on the grid and label it D.
  3. Locate the point (0, 5) on the grid and label it E.

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. point A, over 2, up 8. point B, over 7, up 4. point C, over 9, up 5. 

Show Solution

A = (2, 8), B = (7, 4), C = (9, 5)

coordinate grid

Problem 2

For each set of points, decide if they lie on a vertical line, a horizontal line, or neither. Plot the points on the grid if it is helpful.

  1. (1,5), (2,5), (3,5)(1, 5),\, (2, 5), \,(3, 5)
  2. (1,1), (2,2), (3,3)(1, 1), \,(2, 2), \,(3, 3)
  3. (6,0), (2,0), (5,0)(6, 0), \,(2, 0), \,(5, 0)

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's.

Show Solution
  1. horizontal line
  2. neither
  3. horizontal line
Lesson 4
Sort Quadrilaterals
Choose Two

  1. Choose two of the quadrilaterals. What are they called?

    3 quadrilaterals, A, B, C.
    3 quadrilaterals, left to right, A, 1 set of parallel sides. B, 1 set of parallel sides, 2 right angles. C, 2 sets of parallel sides, opposite sides equal lengths, 4 right angles. 

  2. Name an attribute the two quadrilaterals share.

    What is one way the two shapes are different?

Show Solution
  1. A: trapezoid, B: trapezoid or right trapezoid, C: rectangle, parallelogram, or trapezoid (based on one of the definitions of trapezoid that is inclusive of parallelograms)
  2. Sample responses:
    • A and B: Both are trapezoids. Only B has right angles.
    • B and C: Both are quadrilaterals that have at least one pair of opposite sides that are parallel and at least one angle that is 90 degrees. However, they are different because C has all angles that are 90 degrees. C also has two pairs of opposite sides that have equal measure.
    • A and C: Both are quadrilaterals that have at least one pair of opposite sides that are parallel. C has two pairs of opposite sides parallel. C has all four angles that are 90 degrees whereas A has four angles that are all different measures.
Lesson 5
Trapezoids
Which Ones Are Trapezoids?
  1. When is a quadrilateral also a trapezoid?

  2. Which of the following shapes are trapezoids?  Explain or show your reasoning.

    6 quadrilaterals.
    6 quadrilaterals. Clockwise from top left. A, 2 sets of parallel sides, opposite sides, equal length. B, 2 sets of parallel sides, all sides, equal length. C, 1 set of parallel sides. D, no parallel sides. E, 1 set of parallel sides, 2 right angles. F, 2 sets of parallel sides, no right angles. 

Show Solution
  1. Sample response: A quadrilateral is a trapezoid if it has at least one pair of opposite sides that are parallel.
  2. A, B, C, E, F. Sample response: All of the shapes except D have at least one pair of opposite sides that are parallel.
Lesson 6
Hierarchy of Quadrilaterals
Rhombuses as Parallelograms

Give an example of a parallelogram that is not a rectangle.

blank grid

Show Solution

Sample response: This rhombus is a parallelogram because its opposite sides are parallel. If I draw a rhombus on a grid I can see that the opposite sides will never meet even if the lines are extended in both directions.

quadrilateral on grid

Lesson 7
Rectangles and Squares
Quadrilaterals in the Venn Diagram

Draw the shape or write the letter for each shape in the correct location on the diagram:

4 quadrilaterals on grid
4 quadrilaterals on grid. A, 2 sets of parallel sides, opposite sides equal length. B, 2 sets of parallel sides, opposite sides equal length, 4 right angles. C, 1 set of parallel sides, 2 right angles. D, 2 sets of parallel sides, opposite sides, equal length.

venn diagram. squares, rectangles, rhombuses all inside of parallelograms. squares inside of rhombuses. parallelograms insides of trapezoids. trapezoids inside of quadrilaterals.

Show Solution

venn diagram. 

Lesson 8
Sort Triangles
All, Some, None of the Triangles

Complete the statements about the triangles below.

3 triangles, labeled A, B, C.
A, B, C have a right angle angle and a horizontal side. A, C have 2 sides with equal lengths. B, C have a vertical side. None have an angle greater than 90 degrees. None have all 3 sides with equal lengths.

  1. All of the triangles ______________________________________________________________.
  2. Some of the triangles __________________________________________________________.
  3. None of the triangles ___________________________________________________________.
Show Solution

Sample responses:

  1. All of the triangles have a right angle or an angle that measures 90 degrees. All of the triangles have a horizontal side.
  2. Some of the triangles have two sides that are the same. Some of the triangles have a vertical side.
  3. None of the triangles have an angle greater than 90 degrees. None of the triangles have all 3 side lengths the same.
Section B Check
Section B Checkpoint
Problem 1

What type of quadrilateral is ABCD? Select all that apply.

​​​​​​

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. Quadrilateral A, B, C, D graphed. A, 3 comma 7. B, 9 comma 7. C, 9 comma 3. D, 3 comma 3.

A.parallelogram
B.rhombus
C.rectangle
D.trapezoid
E.square
Show Solution
A, C, D
Problem 2

  1. Which of the triangles are right triangles?

    4 triangles, from left to right. A, two equal sides, one right angle. B, two equal sides. C, no equal sides. D, no equal sides, one right angle.

  2. Which of the triangles have 2 equal side lengths?
Show Solution
  1. A, D
  2. A, B
Problem 3

Fill in each blank with “always,” “sometimes,” or “never” to make each statement true.

  1. A parallelogram is _______________________ a rectangle.
  2. A rectangle is _______________________ a square.
  3. A square is _________________________ a quadrilateral.
Show Solution
  1. sometimes
  2. sometimes
  3. always
Lesson 9
Generate Patterns
Patterns and Relationships

  1. Complete each table with the first 10 numbers of these 2 patterns.

    Jada’s rule: Start with 0 and keep adding 5.

  2. Priya’s rule: Start with 0 and keep adding 10.
  3. What number will be in Priya’s pattern when Jada’s pattern has 100?
  4. What relationship do you notice between corresponding numbers in the two patterns?
Show Solution

  1. 0, 5, 10, 15, 20, 25, 30, 35, 40, 45

    0, 10, 20, 30, 40, 50, 60, 70, 80, 90

  2. 200
  3. Sample response: Priya’s numbers are double Jada’s numbers or Jada's numbers are half Priya's numbers.
Lesson 10
Interpret Relationships
Jada’s and Priya’s Patterns

  1. Jada and Priya created rules for patterns. Complete each table with the first 10 numbers of their pattern.

    Jada’s rule: Start with 0 and add 3.

    rectangle partitioned vertically into 10 equal sized rectangles
    Priya’s rule: Start with 0 and add 4.
    rectangle partitioned vertically into 10 equal sized rectangles
  2. Kiran says that when Jada’s number is 45, Priya’s corresponding number will be 90. Do you agree? Why or why not?
Show Solution

  1. 0, 3, 6, 9, 12, 15, 18, 21, 24, 27

    0, 4, 8, 12, 16, 20, 24, 28, 32, 36

  2. No. Sample response: I don’t agree because 90 is not a multiple of 4 so it's not on Priya's list.
Lesson 11
Patterns and Ordered Pairs
2 Rules

  1. Use the rules to complete the table.

    A B C D
    Rule 1: Start at 0. Add 3.
    Rule 2: Start at 0. Add 6.
  2. What relationships do you notice between corresponding terms in the two patterns?

  3. Plot and label the points on the coordinate grid.

    Coordinate plane. Horizontal axis, rule 1, 0 to 20, by 1's. Vertical axis, rule 2, 0 to 20, by 1's. 

Show Solution
  1. A B C D
    Rule 1: Start at 0. Add 3. 0 3 6 9
    Rule 2: Start at 0. Add 6. 0 6 12 18
  2. Sample response: The numbers with Rule 2 are twice as large as the corresponding numbers with rule 1. The numbers with Rule 1 are 12\frac{1}{2} the corresponding numbers with rule 2.
  3.  

    coordinate plane

Lesson 12
Represent Problems on the Coordinate Grid
Half Dollar

The coordinate grid shows the weight of some half dollars.

Coordinate plane. A, B plotted.
Coordinate plane. Horizontal axis, number of half dollars, 0 to 10, by 1's. Vertical axis, total weight in grams, 0 to fifty, by 5's. A, 2 comma 25. B, 3 comma 37.

Pick one of the points and describe what it represents.

Show Solution

A. 2 half dollars weigh 25 grams.

B. 3 half dollars weigh 37.5 grams (or 37 grams or 38 grams).

Lesson 13
Perimeter and Area of Rectangles
Area and Perimeter of a Rectangle

The point represents the length and width of a rectangle.

Coordinate plane. Horizontal axis, length in centimeters, 0 to 10, by 1's. Vertical axis, width in centimeters, 0 to 10, by 1's. Point, 4 comma 5.

  1. What are the area and perimeter of the rectangle? Explain or show your reasoning.
  2. What is a point that represents a different rectangle with the same area? Explain or show your reasoning.
Show Solution

  1. Area: 20 square centimeters. Sample response: 4×5=204 \times 5 = 20

    Perimeter: 18 centimeters. Sample response: (2×4)+(2×5)=18(2 \times 4) + (2 \times 5) = 18

  2. Sample responses: (2,10)(2, 10), (10,2)(10, 2), (2.5,8)(2.5, 8), (8,2.5)(8, 2.5)
Lesson 14
Copies of Figures
No cool-down
Section C Check
Section C Checkpoint
Problem 1

Lin and Priya create patterns with these rules. Lin’s rule is start with 0 and keep adding 2. Priya’s rule is start with 0 and keep adding 4.

Lin 0 2 4 6 8 10
Priya 0 4 8 12 16 20
  1. What number will be on Priya's list when Lin's number is 26? Explain or show your reasoning.
  2. What number will be on Lin’s list when Priya’s number is 240? Explain or show your reasoning.

  3. Plot the points from the table on the coordinate grid.

    Coordinate plane. Horizontal axis, Lin's pattern, 0 to 30, by 2's. Vertical axis, Priya's pattern, 0 to 30, by 2's. 

Show Solution
  1. 52, because Priya's numbers are twice the corresponding numbers on Lin's list.
  2. 120, because Lin's numbers are half the corresponding numbers on Priya's list.

  3. coordinate plane
Problem 2

Here is some data for the height and age of children in Clare’s neighborhood. 

Coordinate plane. Horizontal axis, age in years, 0 to 14, by 1's. Vertical axis, height in inches, 0 to seventy, by 5's. 13 points plotted.
Coordinate plane. Horizontal axis, age in years, 0 to 14, by 1's. Vertical axis, height in inches, 0 to seventy, by 5's. 13 points plotted. 0 comma 22 point 5. 1 comma 26. S, 1 comma 30. 2 comma 38. 3 comma 36. 3 comma 42. 5 comma 40. 5 comma 44. 5 comma 49. 7 comma 47. 9 comma 48. 11 comma fifty 7 point 5. 12 comma sixty.

  1. Clare’s brother is 5 years old and has a height of 49 inches. Label the point that represents Clare’s brother B.
  2. The point S represents Clare’s sister. How tall is Clare’s sister? How old is Clare’s sister?
Show Solution
  1. coordinate grid
  2. Clare’s sister is 30 inches tall and is 1 year old.