Tips for Instruction

1. Simplify math expressions by using the order of operations.
   • First, do all math operations that lie within parentheses.
   • Working from left to right, do all multiplication and division.
   • Finally, working from left to right, do all addition and subtraction.
2. Understand and use rate, ratio, and proportion.
   • Rate shows the relationship between numbers with different units, usually between some quantity and time (e.g., km/h for speed of driving or dollars/hour for rate of pay).
   • Ratio is a fraction that shows how many times bigger or smaller one number is than another (e.g., when making bannock, the ratio of flour to water is 2 to 1 or 2:1 expressed as a ratio; this means you use twice as much flour as water in the recipe).
   • Proportion shows the relationship between two ratios. Two ratios that look different (4/8 and 8/16), but are actually equal proportions (both are equal to ).
3. Demonstrate the slide of a geometric shape.
   • A slide is when an object has the same shape and orientation, but has been moved to a different location through a shift up, down, forward, back, right, or left.
4. Demonstrate a rotation or turn of a geometric shape.
   • A rotation or turn of an object occurs when the geometric shape is turned at an angle (usually 45, 90, or 180 degrees) on a central point of axis.
5. Demonstrate a flip of a geometric shape.
   • A flip of an object occurs when the geometric shape is reflected or mirrored.
6. Demonstrate knowledge of symmetry in geometric shapes.
   • One demonstration of symmetry is when an object is folded in half and both sides of the object are equal. Symmetry occurs in squares, equilateral triangles, and regular polygons such as hexagons and octagons. A cut-out paper heart is also symmetrical.
   • Rotational symmetry occurs when a shape remains the same when it is rotated on a central point of axis. Of the above shapes, only squares, equilateral triangles, and polygons have rotational symmetry. A heart does not have rotational symmetry because it changes shape when it is rotated on a central point of axis.
7. Understand and use problem-solving skills.
   • Think about how to solve the problem based on prior knowledge and experience with a similar problem.
   • Examine the problem carefully to determine which information is useful and which information is not needed or is missing.
   • Identify the words that signal the use of specific mathematical operations (e.g., the word "into" often indicates that division is needed to solve the problem; "of" often signals that multiplication is needed).
   • Plan how to solve the problem by choosing the appropriate strategy and then writing out, drawing, or saying the plan.
   • Use the plan to solve the problem.
   • Reflect on the solution.
     • Are the numerical calculations correct?
     • Is the solution reasonable given the information provided?
     • Is the solution reasonable given your own estimation or guess as to the answer?
8. Fahrenheit is still used in many countries, including the United States. For example, zero degrees Celsius (freezing) is 32 degrees Fahrenheit.