EQAO preparation by strand
Grade 6 Mathematics
Prepared by: Pauline Martin and Michelle Parrish
Adapted from www.eqao.com in preparation for grade 6 testing (pre-2020 curriculum)
Keewatin Patricia District School Board, January 2013
Please use “File” + “Make a copy”
Grade 3 | Grade 6 |
EQAO preparation by strand
Grade 6 Mathematics
Prepared by: Pauline Martin, KPDSB Numeracy Facilitator/Mathematics SAT
Adapted from www.eqao.com in preparation for grade 6 testing
Keewatin Patricia District School Board, January 2013
This resource is intended for classroom use and as practice for your students.
Each strand has questions from the past 5 years of EQAO tests (2012, 2011, 2010, 2009, and 2008) in the order that they occur in the assessment. Each question is coded by the strand and overall expectation number, assessment year, and booklet and question number as it appeared in the assessment. For example: NV1 TH 2012 Booklet 1 #7 means Number Sense Overall Expectation #1, achievement chart category Thinking (also called Problem Solving in the earlier assessments) from the 2012 assessment in the first booklet and problem number seven. Should you wish to search out the sample student work to use as exemplars for assessment with your students, you can access the full solutions on the EQAO website. http://www.eqao.com/Educators/Elementary/036/036.aspx?Lang=E&gr=036
Multiple choice and open response have not been separated within a strand. Additional space has been removed for open response questions in the interest of keeping this document as short as possible. Keep in mind that open response questions always provide a full page of working and thinking space.
When practicing multiple choice problems with your students, it might be helpful to encourage students to show their thinking in the space you provide. This will help in developing strategies for solving problems when incorrect answer can be eliminated just by their reasonableness, or lack thereof.
Please notice that although a problem appears in only one strand, there is usually a connection/strategy/skill that can be linked to another strand.
For example,
· probability problems almost always use fraction strategies (number sense)
· patterning problems often involve a number pattern that requires skip-counting or multiplication strategies (number sense)
Integrating these problems in a unit of study will provide opportunity for students to think beyond the specific expectations of the unit and make connections to other strands throughout the school year.
Since the problems have been converted from PDF into Word and Google Docs, you should be able to use assistive technology to practice reading with these questions in anticipation of the same technology’s use in the EQAO assessment. Keep in mind that large numbers without commas, like 1 000, will be read as “one zero zero zero” and not “one thousand”. I thought it was important to preserve the integrity of the test’s presentation rather than adjust it to be read correctly.
If you have any suggestions or questions, please feel free contact me.
pauline.martin@kpdsb.on.ca
GEOMETRY
AND SPATIAL SENSE
Geometry and Spatial Sense
GV1 – classify and construct
Polygons and angles.
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 TH 2012 Booklet 1 # 12 Karim is dividing the angle shown below into smaller equal angles. The first of the smaller angles is shaded.
How many smaller angles can Karim make in total?
a 60
b 12
c 10
d 6
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 AP 2011 Booklet 2 #28 Use the line segments AB and BC below to construct pentagon ABCDE with the following properties:
• a right angle at point C
• an angle that measures 110o at point A
• a side of 4.7 cm
Label all angles and sides with their measures.
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 AP 2012 Booklet 2 #10 Consider the geometric shapes below.
Sort these shapes. Write their labels in the correct sections of the Venn diagram below.
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 PS 2011 Booklet 2 #30 Consider the shapes below.
Which list shows the shapes in order from fewest to most lines of symmetry?
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 PS 2010 Booklet 1 #17 A polygon has 4 sides. Two of the sides are parallel and two are not.
What shape is the polygon?
a square
b rhombus
c trapezoid
d parallelogram
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 KU 2010 Booklet 1 #18 Which angle appears to measure 140°?
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 AP 2009 #7 Construct a pentagon on the grid below that meets the following conditions.
• exactly 1 line of symmetry
• 2 obtuse angles
• 2 right angles
• 1 acute angle
• at least 1 side with a length of 3 units
Draw the line of symmetry on your pentagon.
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 KU 2009 #17 Points A, B, and C lie on a line in the polygon shown below.
Which table best classifies the angles of the polygon?
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 PS 2009 #18 A regular polygon is created with angles of 60° and sides of 4 cm in length.
Which statement below describes this polygon?
a triangle with perimeter of 12 cm
b triangle with perimeter of 16 cm
c rhombus with perimeter of 12 cm
d rhombus with perimeter of 16 cm
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 2008 #17 Which is closest to the measure of angle X in ⃤ XYZ? Use a protractor.
a 35°
b 55°
c 90°
d 145°
Geometry and Spatial Sense
GV1 – classify and construct polygons and angles.
GV1 2008 #30 Using a protractor and a ruler, construct a parallelogram with an angle measure of 115° and sides with lengths of 7 cm and 6 cm. Mark on the parallelogram the length of each side and the measure of all angles.
Show your work.
Geometry and Spatial Sense
GV2 – sketch three-dimensional figures, and construct three-dimensional figures from drawings.
Geometry and Spatial Sense
GV2 – sketch three-dimensional figures, and construct three-dimensional figures from drawings.
GV2 KU 2012 Booklet 1 #6 Look at the figure below.
Which of the following is a top view of the figure?
Geometry and Spatial Sense
GV2 – sketch three-dimensional figures, and construct three-dimensional figures from drawings.
GV2 KU 2011 Booklet 2 #23 The three-dimensional figure below was built using cubes.
What is the top view of this figure?
Geometry and Spatial Sense
GV2 – sketch three-dimensional figures, and construct three-dimensional figures from drawings.
GV2 AP 2010 Booklet 1 #7 Sydney makes the figure below with 6 linking cubes.
Draw a top, a front and a side view of Sydney’s figure on the grid.
Geometry and Spatial Sense
GV2 – sketch three-dimensional figures, and construct three-dimensional figures from drawings.
GV2 2008 #18 The three-dimensional figure below has been built using cubes.
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 TH 2012 Booklet 1 #15 The shape on the grid below goes through the following 3 transformations in order:
• rotation of 180° about Point T
• reflection across the mirror line
• translation 5 units left
Which shaded shape is the result?
a Shape 1 b Shape 2 c Shape 3 d Shape 4
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3AP 2012 Booklet 1 #11 Kelly is drawing a rectangle on the grid below.
What are the coordinates of the missing vertex?
a (11, 7)
b (7, 11)
c (11, 6)
d (6, 11)
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 AP 2012 Booklet 2 #11 Consider the border around the picture below.
Transform Shape A to cover the border with no gaps or overlaps. Draw any lines of reflection or points of rotation.
Complete the chart for the first 3 transformations you have drawn. Include directions of rotation or units of translation.
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 AP 2011 Booklet 1 #3 Look at Triangle 2 in the following design.
Which triangle shows Triangle 2 after a rotation of 180° about the centre point?
a Triangle 1
b Triangle 2
c Triangle 3
d Triangle 4
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 PS 2011 Booklet 1 #10 Liam creates a shape using the ordered pairs A(1, 4), B(1, 8), C(4, 8) and D(6, 4).
Draw Liam’s shape on the grid below.
Draw a shape on the grid that is congruent to Liam’s. Start with the ordered pairs E(7, 6) and F(7, 1). Write the coordinates of your shape’s other 2 vertices. (_____,_____) (_____, _____)
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 PS 2011 Booklet 1 #13 The following graphs show the pattern for a triangle that grows in size.
If the pattern continues, what will be the coordinates of Y and Z for Triangle 4?
a Y(8, 3) Z(2, 10)
b Y(3, 8) Z(10, 2)
c Y(3, 8) Z(11, 2)
d Y(8, 3) Z(2, 11)
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 PS 2010 Booklet 1 #6 Shape P is reflected across the dotted line and then rotated 90o clockwise.
Which shape in the diagram below is an image of Shape P after these two transformations?
a Shape 1 b Shape 2 c Shape 3 d Shape 4
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3AP 2010 Booklet 1 #16 Polygon PQRT is rotated 90° clockwise about Point Q.
What are the new coordinates of Point R after this rotation?
a (6, 7)
b (7, 6)
c (11, 2)
d (11, 6)
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 PS 2010 Booklet 2 #29 The diagram shows a square that was moved by a
transformation from position A to position B.
Describe three different ways to move the square from position A to position B.
Each way should use a different type of transformation.
Remember to include the mirror lines or the centre of rotation on the grid.
Complete the following chart.
Type of Transformation | Description |
| |
| |
| |
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 AP 2009 #16 Look at the ladybug below.
The ladybug is rotated three times in the following order.
• 90° counter-clockwise
• 180° clockwise
• 180° clockwise
Which of the following best illustrates the ladybug’s position after the three rotations?
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 PS 2009 #26 The shape below is reflected across the dotted line and then rotated 90°clockwise about point X.
Which of the following shows the shape after the two transformations?
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 AP 2009 #30 Plot and label the following points to form parallelogram PQRS on the grid below.
P (9, 12)
Q (9, 8)
R (7, 6)
S (7, 10)
Rotate parallelogram PQRS 90° counter-clockwise about point R. Draw the new parallelogram on the grid above.
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 2008 #7 Mr. Lee moves a gym mat using the following four transformations.
1. Rotate the gym mat 90° clockwise about Point C.
2. Translate the gym mat 8 units to the right.
3. Translate the gym mat 6 units up.
4. Reflect the gym mat over line AB.
On the grid below, show the new location of the gym mat
after Mr. Lee makes the four transformations.
Show all your work.
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 2008 #16 Triangle ABC is graphed on the grid below.
Triangle ABC is translated 3 units to the left and 4 units down.
What are the new coordinates of Point C?
a (3, 9)
b (7, 3)
c (8, 5)
d (9, 3)
Geometry and Spatial Sense
GV3 – describe location in the first quadrant of a coordinate system, and rotate two-dimensional shapes.
GV3 2008 #26 Look at the figures below.
Which of the following describes how Parallelogram A was moved to create Parallelogram B?
a a reflection over line l
b a translation 3 units to the right
c a translation 3 units to the left, then a reflection over line l
d a translation 3 units to the right, then a reflection over line l