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
PATTERNING
AND ALGEBRA
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns (where the terms are whole numbers), and investigate repeating patterns involving rotations.
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 KU 2012 Book 1 # 4 The 4 terms of the pattern below are made of equilateral triangles with side lengths of 2 units.
Which number sequence represents the perimeters of the 4 terms of this pattern?
a 1, 2, 3, 4
b 3, 4, 5, 6
c 6, 8, 10, 12
d 6, 10, 14, 18
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 TH 2012 Booklet 2 #9 Pattern A is created by repeating the 4 terms below in order.
Pattern B is created by repeating the 3 terms below in order.
Find a term in both patterns that is the same and has the same term number. Show your work.
The term number is __________________________ .
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2012 Booklet 2 #16 Consider the pattern rule below.
Start at 1, and then triple the term to get the next term.
Which graph represents this pattern?
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 TH 2012 Booklet 2 # 18 The chart below shows the first 4 terms of 4 non-repeating patterns.
If the 4 patterns continue, which pattern will reach 30 first?
a Pattern W
b Pattern X
c Pattern Y
d Pattern Z
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 KU 2011 Booklet 1 #1 Consider the pattern below.
7, 14, 28, 56, ____, 224
What is the missing term in this pattern?
a 84
b 102
c 112
d 168
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2011 Booklet 1 #6 Manny uses tiles to build the geometric pattern shown below.
Which of the following represents the number of squares in Stages 4, 5 and 6 of Manny’s pattern?
a 17, 24, 31
b 13, 17, 24
c 13, 17, 21
d 12, 16, 20
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2011 Booklet 2 #25 The graph below shows a relationship between the number of tasks Cole completes and the number of tokens he earns.
According to the pattern shown on the graph, how many tasks must Cole complete to earn 16 tokens?
a 6
b 8
c 16
d 32
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 PS 2011 Booklet 2 #29 Karen and Riley create the shrinking patterns shown below.
What are their pattern rules?
Karen’s rule:___________________________ .
Riley’s rule: __________________________ .
Which pattern will be the first to reach a term smaller than 10? Justify your answer.
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2010 Booklet 1 #2 Emily makes a table of values using the following rule:
Start with 2 and add 3 to get the next term.
Which ordered pair belongs in her table of values?
a (4, 8)
b (4, 9)
c (4, 11)
d (4, 14)
Term Number | Term |
1 | 2 |
| |
| |
| |
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 PS 2010 Booklet 1 #15 The table shows the widths and heights of 5 towers made of blocks.
If the towers continue to be built using the same pattern, for which tower
will the difference between the width and the height be 7 blocks?
a Tower 7
b Tower 8
c Tower 9
d Tower 10
Tower | Width (number of blocks) | Height (number of blocks) |
1 | 3 | 2 |
2 | 5 | 5 |
3 | 7 | 8 |
4 | 9 | 11 |
5 | 11 | 14 |
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2010 Booklet 2 #20 The 4 arrows below repeat in this order to make a pattern.
Which arrow is the 74th term?
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2010 Booklet 2 #25 Sara draws shaded squares on separate pieces of paper.
The areas of the first three shaded squares are shown on the right.
If this pattern continues, what will the area of the 6th shaded square be?
a 2.25 cm2
b 4.5 cm2
c 9 cm2
d 18 cm2
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2010 Booklet 2 #26 The table below shows the number of pennies Anne places in a jar each day.
The pattern continues. Complete the table for Days 5 and 6.
On what day will Anne place 1024 pennies in her jar?
Justify your answer.
Anne will place 1024 pennies in her jar on Day _______.
Anne’s Jar | |
Day | Number of pennies placed in jar |
1 | 1 |
2 | 2 |
3 | 4 |
4 | 8 |
5 | |
6 | |
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 KU 2010 Booklet 2 #30 Consider the following pattern rule.
Triple each term to get the next term. Which pattern matches this rule?
a 0, 3, 6, 9, 12
b 0, 3, 9, 27, 81
c 1, 3, 9, 27, 81
d 1, 4, 7, 10, 13
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 KU 2009 #6 Consider the five terms in the following pattern.
If the pattern continues in the same way,
how many circles will be in the seventh term?
a 21
b 25
c 28
d 36
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 PS 2009 #9 Ms. Lewis has 50 blocks. She uses 22 of these blocks to make the pattern shown below.
How many stages will Ms. Lewis be able to complete with the 50 blocks?
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 KU 2009 #14 Which rule describes the following pattern?
1, 2, 4, 8
a Start with 1 and add 1 to find the next term.
b Start with 1 and add 2 to find the next term.
c Start with 1 and divide by 2 to find the next term.
d Start with 1 and multiply by 2 to find the next term.
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2009 #24 A repeating pattern is shown below.
What is the 16th figure in the pattern?
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 AP 2009 #25 Anya shows a pattern on the grid below.
If the pattern continues in the same way, which coordinates represent a point in this pattern?
a (6, 11)
b (6, 12)
c (7, 11)
d (7, 12)
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 2008 #6 What is the missing term in the decreasing pattern below?
532, 515, ___, 481, 464
a 497
b 498
c 499
d 500
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 2008 #14 A pattern that increases when the same amount is added to each term is represented in the table below.
Which of the following is the term number when the term value is 53?
a 6
b 8
c 41
d 47
Term Number | Term Value |
1 | 11 |
2 | 17 |
3 | 23 |
4 | 29 |
5 | 35 |
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 2008 #15 Look at the repeating pattern below.
R R B B G G Y Y R R B B G G Y Y
If the pattern continues, what will the 82nd letter be?
a R
b B
c G
d Y
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 2008 #24 Which rule describes this numerical pattern?
17, 33, 65, 129, ... To each term,
a add 16 to get to the next term.
b subtract 16 to get to the next term.
c multiply by 2, and add 1 to get to the next term.
d multiply by 2, and subtract 1 to get to the next term.
Patterning and Algebra
PV1 – describe and represent relationships in growing and shrinking patterns
(where the terms are whole numbers), and investigate repeating patterns involving rotations.
PV1 2008 #28 The graph below shows the relationship between the number of sides of a polygon and the sum of the interior angles of that polygon.
• On the grid above, extend the pattern for polygons with 6 sides, 7 sides and 8 sides.
• Sam states that the rule to determine the sum of the interior angles of a polygon is “subtract 2 from the number of sides and multiply this difference by 180.” Is Sam’s rule correct?
Justify your answer.
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 KU 2012 Book 1 #3 If the equation x + 4 = 12 is true, which of the following best describes the variable x?��a one unknown value��b two unknown values��c three unknown values��d many unknown values�
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 AP 2012 Booklet 2 #1 If n x a = 24 and n x a + b = 33, what is the value of b?
a 3
b 4
c 6
d 9
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 AP 2012 Booklet 2 #2 Consider the pattern below.
1161, 387, 129, 43
Which is its pattern rule? To get the next term,
a divide each term by 3.
b divide each term by 4.
c subtract 86 from each term.
d subtract 774 from each term.
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 KU 2011 Booklet 1 #14 Consider the equation below.
5 x n + 12 = 32
What is the value of n in this equation?
a 3
b 4
c 15
d 17
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 AP 2011 Booklet 2 #22 If 6 x a = 12 and 6 x a - b = 8 , what is the value of b?
a 2
b 4
c 6
d 8
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 PS 2011 Booklet 2 #31 Consider the equation below.
3 x m + 2 x n = 36
Which values of m and n would not make the equation true?
a m = 2, n = 15
b m = 4, n = 12
c m = 6, n = 9
d m = 8, n = 7
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 KU 2010 Booklet 1 #14 Look at the equation below.
y ÷ z = 9
Which values of y and z do not make the equation true?
a y = 27; z = 3
b y = 54; z = 6
c y = 63; z = 7
d y = 72; z = 9
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 AP 2009 #5 If a + c = 24, what is the value of e in the equation a + c + e = 27?
a 3
b 9
c 15
d 51
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 PS 2009 #15 If 6 X a = 54 and b - a = 14, what is a X b?
a 34
b 45
c 126
d 207
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 2008 #5 Consider the three equations below.
m + 9 = 12
m + n + 9 = 14
m + n + p = 15
What is the value of p?
a 3
b 4
c 5
d 8
Patterning and Algebra
PV2 – use variables in simple algebraic expressions and equations to describe relationships.
PV2 2008 #25 The total number of books Mitzi reads over the summer can be found using the expression
2 X n + 3, where n represents the number of weeks. After how many weeks will she have read 11 books?
a 3
b 4
c 7
d 8