Mathematics HOW TO HELP YOUR CHILD SUCCEED IN SCHOOL E D U C A T I O N. Dear Parent/Guardian:

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HOW TO HELP YOUR CHILD SUCCEED IN SCHOOL Mathematics 7 Dear Parent/Guardian: Patterns and Relations (identifying patterns You play an important part in helping your child and relationships and

To assist you in your role, this Shape and Space (learning about and using booklet measurement units; and understanding and describes what your son or daughter is expected applying principles of

1 HOW TO HELP YOUR CHILD SUCCEED IN SCHOOL Mathematics 7 Dear Parent/Guardian: Patterns and Relations (identifying patterns You play an important part in helping your child and relationships and applying them) succeed in school. To assist you in your role, this Shape and Space (learning about and using booklet measurement units; and understanding and describes what your son or daughter is expected applying principles of geometry) to learn in mathematics by the end of grade 7, and Data Management and Probability (collecting data, displaying it with graphs, and interpreting provides practical ideas for helping your child data; and describing the likelihood of events) develop mathematically. Photo from Math Makes Sense Pearson Education Canada 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 problemsolving, reasoning and communication skills. 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) E D U C A T I O N 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.

Number and Operations represent repeated multiplication by using exponents 5 x 5 x 5 = 5 3 rename numbers using exponential, standard and expanded forms, and scientific notation Standard form: 125

2 Number and Operations represent repeated multiplication by using exponents 5 x 5 x 5 = 5 3 rename numbers using exponential, standard and expanded forms, and scientific notation Standard form: Exponential form: 50 3 Expanded form: 1 x x x 10 3 Scientific notation: 1.25 x 10 5 solve and create problems involving common factors and common multiples, including those involving greatest common factors (GCFs) and least common multiples (LCMs) 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 9 out of 10 might be expressed as 9:10 ratio 90% percent 9 10 fraction 0.9 decimal compare and order fractions, decimals and integers An integer is any positive or negative whole number. Number Factors Multiples 12 1,2,3,4,6,12 12,24,36,48,60, ,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. develop and apply divisibility rules for 3, 4, 6 and 9 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.) Photo from Math Makes Sense Pearson Education Canada 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 2

3 understand the properties of operations involving decimals and integers, and apply the order of operations When several operations are presented in a number sentence, the order of operations dictates which operations must take place before others. Given x 5, the order of operations dictates that 3 must be multiplied by 5 before 2 is added. explain the difference between algebraic expressions and algebraic equations An algebraic equation (e.g., 2m + 5 = 8 - m) shows that two algebraic expressions (in this case, 2m + 5 and 8 - m) are equal. solve by systematic trial, and illustrate solutions for, simple single-variable linear equations 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 To evaluate 3m + 1 when m = 6, calculate 3 x = 19. distinguish like and unlike terms, and add and subtract like terms Examples: 4n, 3n like terms Patterns and Relations 5x, 2y unlike terms describe simple patterns using words, tables, graphs, algebraic expressions and equations, and use such descriptions to make predictions 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 graph linear equations using tables of values, and interpolate and extrapolate using graphs linear equation a = 2b+1 a interpolate extrapolate table of values b a b graph of the selected values show above predict values between known values predict values beyond the range of known values 3

4 determine if an ordered pair is a solution to a linear equation 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 ) construct and analyze graphs to show how a change in one quantity affects a related quantity Shape and Space use appropriate units to measure, estimate and solve problems involving length, area, volume, capacity, mass and time use rate to solve measurement problems determine and use angle and side length relationships in triangles The longest side of a triangle is opposite the greatest angle. construct angle bisectors and perpendicular bisectors identify angle pair relationships x and y are a pair of supplementary angles. Their sum is 180. y use angle relationships to find angle measures x If you travel at an average rate of 80 km/h for 30 minutes, how far will you travel? understand the relationships among diameter, radius and circumference of a circle, and use the relationships to solve problems circumference - the distance around the outside, or perimeter, of a circle After measuring several triangles, one could conclude that the angles of any triangle add up to 180. This generalization 100 could then be used to find the size of 47 the third angle in a? triangle such as the one at right. determine which combinations of triangle classifications are possible Classification of Triangles by angle by side acute scalene right isosceles obtuse equilateral Sample Question: Can an obtuse triangle also be an isosceles triangle? 4 Photo from Math Makes Sense Pearson Education Canada

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 A read and make inferences from

5 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 A 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 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) image of A Figure A is reflected and then rotated to reach its image position. Data Management and Probability 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 identify situations for which the probability would be near 0, 1, 1 and 1 4 solve probability problems by experiment and using the theoretical definition of probability; compare experimental and theoretical results 2 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. Photo from Math Makes Sense Pearson Education Canada Example of a histogram: Lengths of Baseball Games 30 frequency time (minutes) 5

6 identify all possible outcomes of two independent events, using tree diagrams and area models Example of a tree diagram: You have three shirts (white, green, ) and two pairs of pants (brown, ). What possible outfits might you choose? Shirt Pants Outfit white green brown brown brown white/brown white/ green/brown green/ /brown / 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? second 60% Tips for Helping at Home You 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 Documents For more detailed information with respect to the mathematics curriculum, the following documents are available, both on-line at anglophone-e.asp and in print form: Mathematics Curriculum Guide - Grade 7 ( reference # ) first 60% Curriculum Outcomes Framework Grade 7 ( reference # ) She would be expected to make both free throws 36% of the time. Mathematics Foundation Document ( reference # ) 6 CNB 3317

Learning Outcomes Framework

Learning Outcomes Framework May 2004 Mathematics Grades 7 9 Learning Outcomes Framework Mathematics Grades 7 9 GRADE 7 Grade 7 GCO A: Students will demonstrate number sense and apply number-theory concepts.