Mr. Giovannini
St. Faustina School
Mississauga, Ontario
MATHEMATICS AT A GLANCE OVERVIEW – GRADE SEVEN
GEOMETRY / MEASUREMENT (25%) 10 weeks
- Recognize/draw/name/describe/define: diagonals of
a polygon, parallel / perpendicular lines, straight /adjacent / reflex
angles
- Draw an estimate of an angle in degrees
- Measure/draw/copy angles (semi-circular protractor)
- Identify/name/list properties/give examples of triangles:
equilateral, isosceles,
scalene, right, acute, obtuse, equiangular
- Find & measure the height / base of any triangle
- Combine 2-D figures to make other figures (2 or 3-D)
- Understand the term similar and the relationships
between sides and angles of similar polygons
- State properties of congruent polygons
- Classify figures using lines of symmetry
- Create patterns / symmetrical shapes using transformations (translations,
reflections, rotations)
- Identify / draw combinations of transformations
- State properties preserved by transformations
- Identify / create tessellating shapes / explain why
- Build 3-D objects / analyze & relate to Euler’s formula
- Find perimeter of regular / irregular polygons and
composite figures (given length of sides)
- Find circumference given radius or diameter
- Compare & estimate area using km2 / hectares
- Know that for a given perimeter the area can vary &
for a given area the perimeter can vary
- Estimate, then use formulas to find areas of squares,
rectangles, triangles,
parallelograms, rhombuses, trapezoids, triangles, spheres
- How doubling, tripling sides of a polygon effects area
- For rectangular prisms: measure, calculate surface area / estimate
volume,
then use formula / relate length, width, height, surface area and volume
- Given volume find dimensions of rectangular prism
- Find volume by measuring displacement of a liquid
- Use known volumes to estimate for irregular objects
- Convert units (1 cm3=1 mL, 1000 cm3=1000 mL=1 L)
- Relate between and know metric prefixes from kilo to milli and use
this to change units (within SI)
PROBLEM SOLVING (15%) 6 weeks
Find out → Choose a strategy → Solve it → Look back
A VARIETY OF TRANSLATION, PROCESS AND REALISTIC PROBLEMS
- Use number sentences / equations
- Work backwards / use patterns / use estimates
- Consider other ways to solve a problem
- Use deductive reasoning / eliminate possibilities
- Recognize sub-problems / hidden information
- Ascertain the meaning of key words
- Consider alternate interpretations
- Make appropriate use of technology
- Explain how solution was obtained (oral / written)
- Judge reasonableness of information and results
- Create / solve problems similar to others solved
- Make predictions and generalizations
- Properly display the results
- Solve problems involving + , -, x ,÷ , whole numbers, fractions,
decimals, rates, ratios, percent, length, area, volume, mass,
capacity, time, time zones, data, more than one operation
DATA MANAGEMENT (10%) 4 weeks
Collect → Organize → Display → Summarize →Interpret
- Acquire data using surveys, questionnaires,
experiments, observation, research, interviews, published information
- Recognize that data are affected by nature of sample, method of
collection, sample size, biases
- Discuss factors that distort results
- Distinguish between /discuss pros and cons of using a sample or
a population
- Use fractional circle graphs, double bar graphs
- Find the range, median, mode of data
- Discuss and choose best method to display data
- Discuss reasonableness of data and results
- Use technology to organize and display data
- List possible outcomes and identify favourable outcomes for a
single event
- Use a fraction to describe probability of a single event
- Predict / calculate probability for repeated experiments
- Simulate real situations using manipulatives
- Calculate the probability of a single event (using concrete materials)
/use a ratio to describe odds
NUMBERS & OPERATIONS (35 %) 14 weeks
- Read and write symbols and words, express orally, compare and/or order
numbers
using place value less than or equal to 1 000 000 000 and ≥ 0.0001
- Decimal notation for numbers > one million
- Place value positions as increasing/decreasing powers of ten
- Round to the nearest unit, ten, hundred or tenth
- Terms: exponent, base, power, squared, cubed
- Expand numerals using powers of ten
- + , - by bridging + , - special fractions
- x , ÷ by halving /doubling, factoring
- x , ÷ using additive or subtractive distribution
- - in parts / parts from wholes / a mixed no. from a whole
- ÷ using a power of ten as a divisor
- Choose between: estimation, mental, calculation, calculator ( +, - , x , ÷ )
- Estimate a sum by clustering
- Estimate to place the decimal ( x , ÷ )
- Estimate square root of a whole number < 100 / recall square root of
any perfect square < 100 / use estimation and repeated squaring on
calculator to find approximate square root
- Find greatest common factor / least common multiple
- Use divisibility rules for 2, 5, and 10
- Perform order of operations in correct order (whole numbers, positive
integer
exponents, parentheses)
- Evaluate in a given base with positive integer exponents
- 2-digit multipliers and divisors
- Real world use of integers and fractions / use number line
- Relate concrete, pictorial, verbal, symbolic for integers and fractions
- Use models, diagrams, manipulatives, pictures, number line, benchmarks,
place
value to compare/order/ illustrate fractions, mixed numbers, decimals,
integers
- Use terms: mixed number, improper fraction
- Understand rational numbers as a: measure, division, ratio
- Find equivalent fractions by expressing in simplest terms
- + , - fractions with unlike denominators using manips and pictures; x , ÷
fractions
using manips and pictures
- Estimate then + , - fractions, mixed numbers, decimals
- Add/subtract integers using manips and diagrams
- Find common denominator of two or more fractions
- Convert mixed numbers to improper fractions v v
- Convert fraction/mixed no. to repeating or terminating decimal and
vice versa
- Multiply / divide decimals (tenths by tenths)
- Use calculator special function keys: additive/multiplicative constant,
decimal, clear display, correct error, clear memory, recall memory
- Use memory function key to evaluate an expression
- Use calculator to +, - , x , ÷ fractions / convert fractions to decimals
and find repeating period of a rational number
- Use calculator to check accuracy / correct errors in various ways
RATIO & PROPORTION (10%) 4 weeks ALGEBRA (5%) 2 weeks
- Ratio to compare 3 quantities / rate for different quantities
- Construct rates / ratios from real-life examples
- Find equivalent rates / ratios (manips, pictures, tables, charts,
x or ÷ each
term by the same whole number)
- Express in words or colon form
- Rename a ratio or rate in lowest terms
- Read/ interpret scale drawings
- Find “best buy” / convert percent to a proper fraction and v v
- Percent as a ratio out of 100 / real-world examples
- Express ratios as percents / decimals (d=factors of 100)
- Convert decimal to whole number percent (<100) v v
- Convert a percent to a proper fraction and v v
- Use equivalence to find the missing element
- Solve problems: tips, taxes, discount and sales price
- Correctly use a variety of ways of expressing products such as
Parentheses, 3 x n, 3n, mn
- Terms: variable, constant, expression, equation
- Evaluate an open expression using whole numbers, fractions, and
decimals to replace one variable
- Evaluate an open expression using whole numbers to replace two variables
- Translate between English & algebraic expression
- Solve word problems (manips, diagrams, patterns, tables)
- Use guess and check or cover up for 1 variable
- Connect to variables in geo/measurement formulas
- Use functions: 1-variable (n → 2 x n ), ordered pairs
- Graph ordered pairs / tables of values (first quadrant)
- Describe slides using coordinates
