how to help your child succeed in school mathematics 7 · 2018-09-10 · how to help your child...

HOW TO HELP YOUR CHILD SUCCEED IN SCHOOL

7MathematicsDear Parent/Guardian:

You play an important part in helping your child succeed in school. To assist you in your role, this booklet

• describes what your son or daughter is expected to learn in mathematics by the end of grade 7, and

• provides practical ideas for helping your child develop mathematically.

The grade 7 mathematics curriculum is built around learning outcomes - statements describing what students are expected to know and be able to do. The outcomes are divided into four, broad content areas:

• Number and Operations (understanding our number system and performing arithmetic operations)

• Patterns and Relations (identifying patterns and relationships and applying them)

• Shape and Space (learning about and using measurement units; and understanding and applying principles of geometry)

• Data Management and Probability (collecting data, displaying it with graphs, and interpreting data; and describing the likelihood of events)

As you can see, school mathematics today has both familiar and new elements. Strong number skills (such as mental arithmetic and paper-and-pencil calculation) continue to be important. As well, other areas of mathematics (such as graphing data and describing the likelihood of events) have increased value in today’s society. Greater emphasis is also placed on the development of students’ problem- solving, reasoning and communication skills.

Students are helped in building their own understandings of mathematical ideas by being active “doers” of mathematics. They also learn the value of mathematics by working with it in everyday situations. It is no longer sufficient simply to drill mathematical facts and procedures.

As you read what students are expected to know and be able to do in mathematics by the end of grade 7, you will find a selection of examples and explanations that make the outcomes clearer.

E D U C A T I O N

Photo from Math Makes Sense © Pearson Education Canada

HOW TO HELP YOUR CHILD SUCCEED IN SCHOOL MATHEMATICS 7

Number and OperationsStudents will

• represent repeated multiplication by using exponents

• rename numbers using exponential, standard and expanded forms, and scientific notation

• solve and create problems involving common factors and common multiples, including those involving greatest common factors (GCFs) and least common multiples (LCMs)

• develop and apply divisibility rules for 3, 4, 6 and 9

• apply patterns to rename numbers from fractions to decimals and vice versa

• understand percent, and write ratios, fractions, decimals and percents in alternative forms, including as expressions of probabilities

• compare and order fractions, decimals and integers

• represent, add, subtract, multiply and divide integers, and solve problems involving them

• use estimation and mental math strategies, as appropriate, in calculations involving integers and decimals

Example: 5 x 5 x 5 = 53

Example:

Standard form: 125 000

Exponential form: 503

Expanded form: 1 x 105 + 2 x 104 + 5 x 103

Scientific notation: 1.25 x 105

Example: A number is divisible by 3 if the sum of its digits is divisible by 3. (For instance, 2157 is divisible by 3 since the sum of its digits, 15, is divisible by 3.)

An integer is any positive or negative whole number.

Example:

Number Factors Multiples

12 1,2,3,4,6,12 12,24,36,48,60,72...

18 1,2,3,6,9,18 18,36,54,72,90...

For the numbers 12 and 18, the common factors are 1,2,3 and 6. This makes 6 the greatest common factor (GCF). As well, the table shows the least common multiple (LCM) to be 36.

Example: 9 out of 10 might be expressed as

9:10 ratio

90% percent

fraction

0.9 decimal

910

2



• understand the properties of operations involving decimals and integers, and apply the order of operations

• estimate the results when fractions are added and subtracted, and multiply mentally a fraction by a whole number

• estimate and determine percents, and solve and create problems involving percent

• create and evaluate simple variable expressions, recognizing the four operations apply as with numerical expressions

• distinguish like and unlike terms, and add and subtract like terms

Patterns and Relations

Students will

• describe simple patterns using words, tables, graphs, algebraic expressions and equations, and use such descriptions to make predictions

• explain the difference between algebraic expressions and algebraic equations

• solve by systematic trial, and illustrate solutions for, simple single-variable linear equations

• graph linear equations using tables of values, and interpolate and extrapolate using graphs

When several operations are presented in a number sentence, the order of operations dictates which operations must take place before others. Example: Given 2 + 3 x 5, the order of operations dictates that 3 must be multiplied by 5 before 2 is added.

To evaluate 3m + 1 when m = 6, calculate 3 x 6 + 1 = 19.

An algebraic equation (e.g., 2m + 5 = 8 - m) shows that two algebraic expressions (in this case, 2m + 5 and 8 - m) are equal.

Examples: 4n, 3n like terms

5x, 2y unlike terms

5p + 8 = 63 is an example of a single-variable linear equation.

To solve it by systematic trial, one might follow steps such as shown at right. By means of a series of trials, one can arrive at the solution, in this case, p = 11.

p 5p + 8 63

9 53 63

10 58 63

11 63 63

Example: linear equation a = 2b+1

2

2

4

6

8

10

12

4 6

b a0 11 32 53 74 9

a

b

table of values

graph of the selected values show above

interpolate predict values between known values

extrapolate predict values beyond the range of known values

3


• determine if an ordered pair is a solution to a linear equation

• construct and analyze graphs to show how a change in one quantity affects a related quantity

Shape and SpaceStudents will

• use appropriate units to measure, estimate and solve problems involving length, area, volume, capacity, mass and time

• use rate to solve measurement problems

• understand the relationships among diameter, radius and circumference of a circle, and use the relationships to solve problems

• determine which combinations of triangle classifications are possible

• determine and use angle and side length relationships in triangles

• construct angle bisectors and perpendicular bisectors

• identify angle pair relationships

• use angle relationships to find angle measures

circumference - the distance around the outside, or perimeter, of a circle

Example: The longest side of a triangle is opposite the greatest angle.

Example: x and y are a pair of supplementary angles. Their sum is 180°.

xy

Classification of Triangles

by angle by side

acute scalene

right isosceles

obtuse equilateral

Sample Question:

Can an obtuse triangle also be an isosceles triangle?

Example: After measuring several triangles, one could conclude that the angles of any triangle add up to 180°. This generalization could then be used to find the size of the third angle in a triangle such as the one at right.

100°

47°?

Example: If you travel at an average rate of 80 km/h for 30 minutes, how far will you travel?

4

In the previous example, each pair of numbers in the table (e.g., (2,5)) is an ordered pair. Each of these pairs is a solution to the given equation, since substituting the values for b and a produces a true statement. (For (2,5) substituting gives 5 = 2 x 2 + 1.)


• explain why the sum of the angles of a triangle is 180°

• sketch and build 3-D objects

• describe and apply translations, reflections and rotations, and their combinations

Data Management and Probability

Students will

• select and use appropriate data collection methods, and distinguish between biased and unbiased sampling, and first- and second-hand data

• formulate questions and statistics projects to explore relevant issues

• construct appropriate data displays, including histograms

• read and make inferences from data displays

• determine mean, median and mode and how they are affected by data changes, and draw inferences based on the variability of data sets

• identify situations for which the probability would be near 0, , and 1

• solve probability problems by experiment and using the theoretical definition of probability; compare experimental and theoretical results


Example: For the data 2, 2, 5, 6, 6, 6, 8

5 = mean (arithmetic average)

6 = median (middle value in rank)

6 = mode (most frequent value)A

image of A

Figure A is reflected and then rotated to reach its image position.

Example:

5

41

21

Example of a histogram:

Lengths of Baseball Games

freq

uen

cy 20

30

10

0 100 120 140 160 180 200 220

time (minutes)

Theoretical probability is a calculation of the expected likelihood of something happening. For example, when rolling a die, the theoretical probability of rolling a two is 1 out of 6 because any one of the six faces has an equal chance of turning up.


• identify all possible outcomes of two independent events, using tree diagrams and area models

Tips for Helping at HomeYou can help your child develop mathematically in many ways. Some sample suggestions:

• Include your child in appropriate budget conversations; encourage estimation and mental calculation.

• Play mathematical games (such as cribbage and chess).

• Take your child shopping; determine unit prices and "best buys".

• Assist your child with reading and interpreting map scales.

• Use appropriate mathematical language (including the use of metric units of measure).

• Assist your child with interpreting graphs that appear in various print media.

Ultimately, it is important to talk to your child's teacher. He or she can best advise you on home activities to meet your child's learning needs.

Related DocumentsFor more detailed information with respect to the mathematics curriculum, the following documents are available, both on-line at www.gnb.ca/0000/anglophone-e.asp and in print form:

• Mathematics Curriculum Guide - Grade 7 (1999 - reference # 843690)

• Curriculum Outcomes Framework Grade 7 (2004 - reference # 844050)

• Mathematics Foundation Document (1996 - reference # 841390)


CNB 33176

Example of an area model:

When playing basketball, Mary makes 60% of her free throws. When taking two free throws, how likely is it she will make both?

She would be expected to make both free throws 36% of the time.

60%

60%

firs

t

second

Example of a tree diagram: You have three shirts (white, green, black) and two pairs of pants (brown, black). What possible outfits might you choose?

Shirt Pants Outfit

brown white/brown black white/black

brown green/brown black green/black

brown black/brown black black/black

white

black

green