Middle Level Mathematics Assessment, June 2008

New Brunswick January, 2006 Middle Level Mathematics Assessment June, 2008

Information Bulletin

Assessment and Evaluation Branch Department of Education New Brunswick

The Department of Education administers a comprehensive Provincial Evaluation Program to monitor overall student achievement at particular points in the system. This provides important feedback at provincial and local levels about students' knowledge and skills. The Middle Level Mathematics Assessment is an important component of this program. It focuses on student performance over the middle school years.

Administration

The Middle Level Mathematics Assessment consists of two sections that will be administered over a two-day period.

Day/Date Section Time Allotment

Monday Section A June 9, 2008 Selected-Response Items 90 minutes

Tuesday Section B June 10, 2008 Part 1: Mental Mathematics 2 minutes Part 2: Non-calculator Mathematics 20 minutes Part 3: Constructed-Response Items 60 minutes

If required, students may have up to 20 minutes additional time to complete Section A or the constructed-response questions in Section B. Up to 10 minutes of additional time may be given to complete the Non-calculator questions in Section B.

Make-up Date: Wednesday, June 11, 2008

Types of Items

Section A of the assessment will consist of selected-response items. Students will be required to select the correct answer from a number of response choices.

Section B is divided into three parts. The first part, Mental Mathematics, consists of 12 questions to be answered during a two-minute time frame. Part 2, Non-calculator Mathematics, consists of a combination of selected-response and constructed-response questions. Students are to determine their own response for the constructed-response questions. Part 3 consists of constructed-response questions. The use of calculators is permitted for this part of the assessment. Sample items are provided in Appendix A.

1 Distribution of Topics

The following Distribution of Topics reflects the approximate percentage emphasis allotted to each strand. A listing of strands and outcomes is presented in Appendix B.

Distribution of Topics

Strands Percent Emphasis Number 50% Number Concepts (15%) Operations (35%) Patterns and Relations 15% Measurement and Geometry 20% Measurement (15%) Geometry (5%) Data Management and Probability 15% Data Management (10%) Probability (5%)

Testing Procedures

The principal of each middle school is responsible for the security of the Middle Level Mathematics Assessment materials sent to his/her school and for ensuring that there is no unauthorized reproduction of these materials.

Approximately two weeks before the assessment, the Administrative Guidelines will be sent to each school. Teachers administering the assessment should read these guidelines carefully prior to the administration date. These guidelines clarify how the assessment is to be administered.

Following completion of the assessment, a checklist is provided on the Packing / Return- Packing Slip to assist the principal in preparing materials for return to the Department of Education.

2 Exemptions

The Middle Level Mathematics Assessment is compulsory for all students presently enrolled in the eighth grade in New Brunswick schools. The assessment is meant to be as inclusive as possible. However, the school principal may request an exemption for a student who is unable to respond with any degree of success to the assessment instrument or if participation would be harmful to the student.

A recommendation for exempting an individual student should be provided using the appropriate form and bearing the required signature(s). Please refer to the document Guidelines for Exemptions and Accomodations for more specific information located at http://www.gnb.ca/0000/publications/eval/guidelin.pdf.

Bilingual Version of the Assessment

A bilingual version of the assessment will be produced for French Immersion students. French Immersion students will be able to respond to any item in French or English so that language does not interfere with their ability to demonstrate proficiency in mathematics.

Formula Sheet

A Formula Sheet will be provided for students when writing the assessment. Refer to Appendix C for the list of formulas that will be provided for students.

Student Use of Calculators

The use of calculators is encouraged for Section A and for the constructed-response questions in Part 3 of Section B. Students should have a calculator that performs addition, subtraction, multiplication, and division as well as having memory, percent, square root, exponent, reciprocal, and +/ keys.

3 Reporting of Results

All parts of the assessment will be scored by the Department of Education. Provincial, district, school and individual results will be generated.

Looking Back: Middle Level Mathematics Assessment, June 2007

Background

In June 2007 of their grade 8 year, students wrote the Middle Level Mathematics Assessment. Although the assessment is based on the grade 8 provincial mathematics curriculum, it is designed to reflect students' achievement over the middle school years.

The assessment included items of varying difficulty levels and addressed the seven strands: Number Concepts, Operations, Patterns and Relations, Measurement, Geometry, Data Management, and Probability.

Student results were reported in terms of three standards: Strong Achievement, Appropriate Achievement, and Below Appropriate Achievement. These standards were linked, in turn, to the percentages of test items answered correctly. The percentage of students achieving these levels is reported based upon the total number of students registered in New Brunswick schools.

Findings

Of the 6475 eighth graders registered in New Brunswick schools, 58% met (39%) or exceeded (19%) the appropriate performance level in mathematics. 59% percent of males and 57% of females met the standard in 2007 as compared to 60% and 56% respectively in 2006.

Students enrolled in the French Immersion programs achieved higher levels than did those in the English program. In 2007, 78% of the French Immersion students met the standard, compared to 47% of those in the English program.

Appendix A: Sample Items

4 Section A, Selected Response

1. Which of the following fractions can be found on the number line 1 3 between and ? 3 4

1 A. 4

2 B. 6

7 C. 8

6 D. 12

GCO*: A7 A. 33% B. 16% C. 4% D. 47%

2. On a map, a 200 km distance is represented by a 4.5 cm line. Using the same scale, how long would a distance of 550 km be?

A. 13.5 cm. B. 12.8 cm. C. 12.4 cm. D. 12.0 cm

GCO: A9 A. 11% B. 15% C. 59% D. 15%

* GCO – General Curriculum Outcome

5 3. The population of New Brunswick is about 760 000 and the population of Canada is about 32 000 000. About what percent of the population of Canada is New Brunswick’s population?

A. 40% B. 25% C. 4% D. 2.5%

GCO: B3 A. 16% B. 15% C. 20% D. 49%

4. The price of CDs at a local music store increased from $16 to $20 for each CD. What was the percent increase?

A. 20% B. 25% C. 75% D. 80%

GCO: B4 A. 35% B. 51% C. 2% D. 12%

1 5. 6 × 3 + 4 × = 2

A. 11 B. 20 C. 21 D. 26

GCO: B10 A. 26% B. 56% C. 5% D. 13%

6 6. Find the value of:

−2.44 - 3 7.99

A. 23.97 B. 21.53 C. - 26.41 D. - 43.47

GCO: B13 A. 4% B. 22% C. 51% D. 24%

7. What is the area of the rectangle?

2 4 A. x + 2x + 4 3 3

B. 4 x + 14 3

C. 5x + 7

D. 6x + 12

GCO: B16 A. 15% B. 17% C. 10% D. 58%

7 8. The chart below shows the price of a phone call to England.

Minutes 1 2 3 4 5

Cost $0.90 $1.30 $1.70 $2.10 $2.50

How much would a 10-minute call cost?

A. $4.00 B. $4.50 C. $5.00 D. $9.00

GCO: C1 A. 3% B. 51% C. 39% D. 7%

9. The area of this shape is about:

A. 18 cm2 B. 28 cm2 C. 36 cm2 D. 110 cm2

GCO: D4 A. 13% B. 43% C. 39% D. 5%

8 10. Use the following key when answering this question.

Shaded is positive. = 1 = x White is negative.

The diagram below represents an equation.

What would be the value of x for this equation?

A. x = −2 B. x = 3 C. x = −4 D. x = 6

GCO: C6 A. 50% B. 26% C. 19% D. 5%

9 11. A certain cube has a surface area of 96 cm2. What is the volume of the cube?

A. 16 cm3 B. 24 cm3 C. 64 cm3 D. 96 cm3

GCO: D8 A. 19% B. 29% C. 39% D. 13%

12. Squares are drawn on each side of the right triangle below. What is the area of the square on DE?

D B A 7 c9m cm

E 5 cm F C A. 8 cm2 B. 49 cm2 C. 56 cm2 D. 64 cm2

GCO: D9 A. 23% B. 19% C. 46% D. 13%

10 13. In the diagram below, each interior angle of the regular pentagon is shaded.

Find the sum of the interior angles of this regular pentagon.

A. 360o B. 540o C. 600o D. 900o

GCO: E4 A. 23% B. 54% C. 15% D. 8%

14. Five students made the following marks on a test:

Student Alexis Nicole Michael Liam Molly Mark (%) 60 60 70 75 90

If Michael’s mark changes from 70 to 60, which measures change?

A. mean, median and mode B. mean C. median D. mean and median

GCO: F7 A. 20% B. 14% C. 9% D. 57%

11 15. What is the probability that the spinner will land on either E or D?

1 A. 3 1 A B. B 4 1 E C. 5 C D 1 D. 6

GCO: G2 A. 46% B. 8% C. 25% D. 21%

12 Section B Part 1: Mental Mathematics (12 questions)

Answer Mean Score

1. 144 = ______12 82%

2. 48 × 25 = ______1200 45%

3. 52.9 × 0.1 = ______5.29 57%

1 4. of 24 = ______8 64% 3

3 4 1 – = 5. 7 7 55%

3 3 3 6. – = 58% 5 10 10

7. 500 – 297 = ______203 69%

8. 1 32 42% 16 ______2

1 7 7 9. × = 59% 6 8 48

10. 5 × 12.7 × 20 = ______1270 42%

11. 0.5 × 486 = ______243 48%

12. 1 3 38% 33 % of 9 = ______3

14 Section B, Part 2: Non-calculator Mathematics

1. The ratio of snowboarders to down-hill skiers is 9:5. If there are only 56 people on the hill, how many are snowboarders? __ 36__

GCO: A9 Mean Score: 46%

2. Use the following key to answer this question.

Shaded is positive. = 1 = x White is negative.

The diagram represents an equation.

What would be the value of x for this equation? _ 2__

GCO: B15 Mean Score : 21%

15 3. Look at the pattern below.

7.0, 5.5, 4.0, 2.5, _____, _____, _____?

If the pattern were to continue, what would the 7th term be? __-2.0__

GCO: C1 Mean Score: 40%

4. The drawing below shows two similar shapes.

15 cm 10 cm

What is the length of side x? __ 8___ cm

GCO: D1 Mean Score: 32%

16 5. A rectangle has a perimeter of 30 cm. Its area is 56 cm2.

What are its dimensions? _7 cm x 8 cm

GCO: D5 Mean Score: 41%

Section B, Part 3: Constructed Response

17 Value: 3 points 1. The area of a rectangle is 12x + 12. Give three different possible dimensions.

1 point for each correct answer Possible correct answers:

1 (12x + 12) or 1 x (12x + 12) 2 (6x + 6) 2 x (6x + 6) 3 (4x + 4) 3 x (4x + 4) 4 (3x + 3) 4 x (3x + 3) 6 (2x + 2) 6 x (2x + 2) 12 ( 1x +1) 12 x ( 1x +1)

a. ______

GCO: B16 Mean Score: 14%

b. ______

c. ______

18 Value: 4 points

2. This graph represents a swimming race between two middle school students. ) s e r t e m (

t n i o p

g n i t r a t s

m o r f

e c n a t s

Kelly a. What was the total distance of the race? _100m .

GCO: C2 Mean Score: 23% 0 30 60 Time (seconds) b. Who had the fastest start in the race? _ Trudy_.

19 c. What does the point X indicate?

Acceptable answers include: Point X indicates the place where they “met up”/ passed each other/ crossed paths No points were awarded for answers like: same race distance/same speed/where Kelly passed Trudy.

d. Who won the race? _Kelly .

20 Section A : Réponses choisies

1 3 1. Parmi les fractions suivantes, laquelle est située entre et sur une 3 4 droite numérique ?

1 A. 4

2 B. 6

7 C. 8

D. 6 12

RAP*: A7 A. 33% B. 16 % C. 4 % D. 47 %

2. Sur une carte, une distance de 200 km est représentée par une ligne de 4,5 cm. Selon la même échelle, combien longue une distance de 550 km serait-elle?

A. 13,5 cm B. 12,8 cm C. 12,4 cm D. 12,0 cm

RAP : A9 A. 11 % B. 15 % C. 59 % D. 15 %

21 * RAP – Résultats d’apprentissage du programme

3. Le Nouveau-Brunswick compte environ 760 000 habitants et le Canada en compte environ 32 000 000. Quel est le pourcentage approximatif de la population du Nouveau-Brunswick par rapport à la population du Canada ?

A. 40 % B. 25 % C. 4 % D. 2,5 %

RAP : B3 A. 16 % B. 15 % C. 20 % D. 49 %

4. Chez un marchand de musique local, le prix des disques compacts est passé de 16 $ à 20 $ l’unité. Quel est le pourcentage d’augmentation?

A. 20 % B. 25 % C. 75 % D. 80 %

RAP : B4 A. 35 % B. 51 % C. 2 % D. 12 %

1 5. 6  3 + 4  = 2

A. 11 B. 20 C. 21 D. 26

RAP : B10 A. 26 % B. 56 % C. 5 % D. 13 %

22 6. Trouve la valeur de :

−2,44 - 3 7,99

A. 23,97 B. 21,53 C. - 26,41 D. - 43,47

RAP : B13 A. 4 % B. 22 % C. 51 % D. 24 %

7. Quelle est l’aire de ce rectangle?

2 4 A. x + 2x + 4 3 3

B. 4 x + 14 3

C. 5x + 7

D. 6x + 12

RAP : B16 A. 15 % B. 17 % C. 10 % D. 58 %

23 8. Le tableau ci-dessous montre le coût d’un appel téléphonique en Angleterre.

Minutes 1 2 3 4 5

Coût 0,90 $ 1,30 $ 1,70 $ 2,10 $ 2,50 $

Combien coûte un appel d’une durée de 10 minutes?

A. 4, 00 $ B. 4, 50 $ C. 5, 00 $ D. 9, 00 $

RAP : C1 A. 3 % B. 51 % C. 39% D. 7 %

9. L’aire de cette figure mesure environ :

A. 18 cm2 B. 28 cm2 C. 36 cm2 D. 110 cm2

24 RAP : D4 A. 13 % B. 43 % C. 39 % D. 5 %

10. Utilise la légende suivante pour répondre à cette question.

Parties ombrées : valeurs positives = 1 = x Parties blanches : valeurs négatives

Le schéma ci-dessous représente une équation.

Quelle est la valeur de x dans cette équation?

A. x = −2 B. x = 3 C. x = −4 D. x = 6

RAP : C6 A. 50 % B. 26 % C. 19 % D. 5 %

25 11. L’aire d’un cube mesure 96 cm2. Quel est le volume de ce cube?

A. 16 cm3 B. 24 cm3 C. 64 cm3 D. 96 cm3

RAP : D8 A. 19 % B. 29 % C. 39 % D. 13 %

12. Des carrés sont construits sur chacun des côtés de ce triangle rectangle. Quelle est l’aire du carré construit sur le côté DE?

D B A 9 cm 7 cm

E 5 cm F C

A. 8 cm2 B. 49 cm2 C. 56 cm2 D. 64 cm2

RAP : D9 A. 23 % B. 19 % C. 46 % D. 13 %

26 13. Sur le schéma ci-dessous, chaque angle intérieur du pentagone régulier est ombré.

Trouve la somme des angles intérieurs de ce pentagone régulier.

A. 360o B. 540o C. 600o D. 900o

RAP : E4 A. 23 % B. 54 % C. 15 % D. 8 %

14. Cinq élèves ont obtenu les notes suivantes lors d’une épreuve :

Élève Alexis Nicole Michael Liam Molly Note (%) 60 60 70 75 90

Si la note de Michael passe de 70 à 60, quelles mesures changeront?

A. la moyenne, la médiane et le mode B. la moyenne C. la médiane D. la moyenne et la médiane

27 RAP : F7 A. 20 % B. 14% C. 9 % D. 57 %

15. Quelle est la probabilité que la flèche s’arrête sur E ou D?

1 A. 3 1 A B. B 4 1 E C. 5 C D 2 D. 5

RAP : G2 A. 46 % B. 8 % C. 25 % D. 21 %

28 Section B, partie 1 : Calcul mental (12 questions) Réponse Moyenne

1. 144 = ______12 82 %

2. 48 × 25 = ______1200 45 %

3. 52,9 × 0,1 = ______5,29 57 %

1 4. de 24 = ______8 64 % 3

3 4 1 – = 5. 7 7 55 %

3 3 3 6. – = 58 % 5 10 10

7. 500 – 297 = ______203 69 %

8. 1 32 42 % 16 ______2

1 7 7 9. × = 59 % 6 8 48

10. 5 × 12,7 × 20 = ______1270 42 %

11. 0,5 × 486 = ______243 48 %

12. 1 3 38 % 33 % de 9 = ______3

30 Section B, partie 2 : À faire sans calculatrice

1. Le rapport entre le nombre de planchistes et le nombre de skieurs est de 9 : 5. S’il y a 56 personnes sur la pente, combien y a-t-il de planchistes? ___36___

RAP : A9 Moyenne : 46 %

2. Utilise la légende ci-dessous pour répondre à la question.

Parties ombrées: valeurs positives = 1 = x Parties blanches: valeurs négatives.

Le schéma ci-dessous représente une équation.

Quelle est la valeur de x dans cette équation? __2__

RAP : B15 Moyenne : 21 %

31 3. Observe la suite ci-dessous.

7,0, 5,5, 4,0, 2,5, _____, _____, _____?

Si cette régularité est maintenue, quel sera le 7e terme? __-2,0__

RAP : C1 Moyenne : 40 %

4. Deux figures semblables sont illustrées ci-dessous.

15 cm 10 cm

Quelle est la mesure du côté x ? __ 8___ cm

RAP : D1 Moyenne : 32 %

32 5. Un rectangle a un périmètre de 30 cm. Son aire mesure 56 cm2.

Quelles sont les dimensions? _7 cm x 8 cm

RAP : D5 Moyenne : 41 %

33 Section B, partie 3 : Réponses construites

Valeur : 3 points

1. L’aire d’un rectangle mesure 12x + 12. Donne trois dimensions différentes possibles.

1 point for each correct answer Possible correct answers:

1 (12x + 12) or 1 x (12x + 12) 2 (6x + 6) 2 x (6x + 6) 3 (4x + 4) 3 x (4x + 4) 4 (3x + 3) 4 x (3x + 3) 6 (2x + 2) 6 x (2x + 2) 12 ( 1x +1) 12 x ( 1x +1)

a. ______

b. ______

c. ______

34 Valeur : 4 points

2. Ce diagramme illustre une course à la nage entre deux élèves d’une école intermédiaire ) s e r t è m (

t r a p é d

t n i o p

r i t r a p

e c n a t

s 50 i

Kelly a. Sur quelle distance ont-elles nagé? _100m .

0 30 60 Temps (secondes) b. Qui a effectué le départ le plus rapide? _Trudy_.

35 c. Que signifie le point d’intersection X sur ce diagramme?

Acceptable answers include: Point X indicates the place where they “met up”/ passed each other/ crossed paths No points were awarded for answers like: same race distance/same speed/where Kelly passed Trudy.

d. Qui a gagné la course? _Kelly_.

36 Appendix B: Grade 8 Mathematics Outcomes

Number Concepts

A1 model and link various representations of square root of a number A2 recognize perfect squares between 1 and 144 and apply patterns related to them A3 distinguish between an exact square root of a number and its decimal approximation A4 find the square root of any number, using an appropriate method A5 demonstrate and explain the meaning of negative exponents for base ten A6 represent any number written in scientific notation in standard form, and vice versa A7 compare and order integers and positive and negative rational numbers (in decimal and fractional forms) A8 represent and apply fractional percents, and percents greater than 100, in fraction or decimal form, and vice versa A9 solve proportion problems that involve equivalent ratios and rates

Operations

B1 demonstrate an understanding of the properties of operations with integers and positive and negative rational numbers (in decimal and fractional forms) B2 solve problems involving proportions, using a variety of methods B3 create and solve problems which involve finding a, b, or c in the relationship a% of b = c, using estimation and calculation B4 apply percentage increase and decrease in problem situations B5 add and subtract fractions concretely, pictorially, and symbolically B6 add and subtract fractions mentally, when appropriate B7 multiply fractions concretely, pictorially, and symbolically B8 divide fractions concretely, pictorially, and symbolically B9 estimate and mentally compute products and quotients involving fractions B10 apply the order of operations to fraction computations, using both pencil and paper and the calculator B11 model, solve, and create problems involving fractions in meaningful contexts B12 add, subtract, multiply, and divide positive and negative decimal numbers with and without the calculator B13 solve and create problems involving addition, subtraction, multiplication, and division of positive and negative decimal numbers

37 B14 add and subtract algebraic terms concretely, pictorially, and symbolically to solve simple algebraic problems B15 explore addition and subtraction of polynomial expressions, concretely and pictorially B16 demonstrate an understanding of multiplication of a polynomial by a scalar, concretely, pictorially, and symbolically

Patterns and Relations

C1 represent patterns and relationships in a variety of formats and use these representations to predict unknown values C2 interpret graphs that represent linear and non-linear data C3 construct and analyse tables and graphs to describe how change in one quantity affects a related quantity C4 link visual characteristics of slope with its numerical value by comparing vertical change with horizontal change C5 solve problems involving the intersection of two lines on a graph C6 solve and verify simple linear equations algebraically C7 create and solve problems, using linear equations

Measurement

D1 solve indirect measurement problems, using proportions D2 solve measurement problems, using appropriate SI units D3 estimate areas of circles D4 develop and use the formula for the area of a circle D5 describe patterns and generalize the relationships between areas and perimeters of quadrilaterals, and areas and circumferences of circles D6 calculate the areas of composite figures D7 estimate and calculate volumes and surface areas of right prisms and cylinders D8 measure and calculate volumes and surface areas of composite 3-D shapes D9 demonstrate an understanding of the Pythagorean relationship, using models D10 apply the Pythagorean relationship in problem situations

38 Geometry

E1 demonstrate whether a set of orthographic views, a mat plan, and an isometric drawing can represent more than one 3-D shape E2 examine and draw representations of 3-D shapes to determine what is necessary to produce unique shapes E3 draw, describe, and apply transformations of 3-D shapes E4 analyse polygons to determine their properties and interrelationships E5 represent, analyse, describe, and apply dilatations

Data Management

F1 demonstrate an understanding of the variability of repeated samples of the same population F2 develop and apply the concept of randomness F3 construct and interpret circle graphs F4 construct and interpret scatter plots and determine a line of best fit by inspection F5 construct and interpret box- and whisker-plots F6 extrapolate and interpolate information from graphs F7 determine the effect of variations in data on the mean, median, and mode F8 develop and conduct statistics projects to solve problems F9 evaluate data interpretations that are based on graphs and tables

Probability

G1 conduct experiments and simulations to find probabilities of single and complementary events G2 determine theoretical probabilities of single and complementary events G3 compare experimental and theoretical probabilities G4 demonstrate an understanding of how data is used to establish broad probability patterns

39 Appendix C: Formula Sheet

40 41 42