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Be sure also to check the Secondary page for general support.
Be sure also to check the Secondary page for general support.
Measurement: 3D objects can be examined mathematically by measuring length, surface area, and volume directly and indirectly.
Measurement: 3D objects can be examined mathematically by measuring length, surface area, and volume directly and indirectly.
UNIT CONVERSION (Imperial)
Use tools to explore relationships
Explain and justify mathematical ideas
Ask your students:
Create a table like the one shown on the right.
Find several long objects around your home (eg: door, counter, couch, etc) and measure their length in inches and feet.
What do you notice about the relationship between inches and feet?
Explain whether 4' 5" is the same as 4.5 feet, or different.
UNIT CONVERSION (Metric vs Imperial)
Use tools to explore relationships
Ask your students:
Find several long objects around your home (eg: door, counter, couch, etc) and measure their length in inches and centimetres.
Create a table like the one above but for inches and centimetres, not feet.
What do you notice about the relationship between inches and centimetres?
COMPARISONS ACROSS UNITS
Solve problems with persistence
Show the image below to your students.
Ask:
Which celebrity is shorter/taller?
How do you know?
What made comparing the two heights challenging?
How did you solve this challenge?
Create other comparison challenges across imperial and metric units for your students to solve. For example:
Vancouver to Montreal: 4554 km vs. San Francisco to New York: 2903 miles
distances from your school to neighbouring schools or local landmarks
Would you rather jog 13 miles or 20 kilometres?
SURFACE AREA VS VOLUME (Same Volume with different Surface Areas)
Apply mathematical undertanding through play and problem solving
Visualize to explore mathematical concepts
Show the image on the right and ask your students to observe the two rectangular prisms. Ask:
Without doing any calculating, how do the volume and surface area of each compare? (e.g. which is greater?)
Calculate the surface area and volume of each. Do the calculations confirm what you expected?
What other rectangular prisms can you make that have the same volume but different surface areas? What is the greatest surface area that you can create?
This task is also available on this handout.
SURFACE AREA VS VOLUME (Same Surface Area with different Volumes)
Apply mathematical undertanding through play and problem solving
Visualize to explore mathematical concepts
Instructions:
The rectangular prism on the right requires 80 square units to paint all 6 faces.
What other rectangular prisms can you make that also require 80 square units to paint all 6 faces?
What is the volume of each of your prisms? What is the greatest volume that you can create?
This task is also available on this handout.
SURFACE AREA & VOLUME of TRIANGULAR PRISMS
Estimate reasonably
Apply mathematical understanding through problem solving
Show the two triangular prisms on the right.
Ask:
Without calculating, estimate how the volume of one prism compares to the other?
Without calculating, estimate how the surface area of one prism compares to the other?
Calculate the surface area and volume of each.
Do the calculations confirm what you expected?How can the volume of the first prism help you to know the volume of the second prism?
Trigonometry:
Proportional reasoning helps us to solve indirect measurement problems.
Trigonometry:
Proportional reasoning helps us to solve indirect measurement problems.
RATIOS
Analyze and apply mathematical ideas through reason
Think with curiosity and wonder when exploring problems
Provide the image on the right and ask your students to observe the two triangles. Ask:
How are the two triangles related?
How does the ratio BC:AB compare to EF:DE?
Explore other ratios within each triangle.
What do you notice?
TRIGONOMETRIC RATIOS
Analyze and apply mathematical ideas through reason
Give students a right triangle with all 3 side lengths shown. An example is on the right.
Ask questions such as:
Determine sinC and tanA.
Which trigonometric ratio is 20/29? Is there more than one?
Which trigonometric ratio is the largest value?
TRIGONOMETRY: Determining Unknown Lengths
Model with mathematics in situational contexts
Reflect on mathematical thinking
Give students one or both of the images shown.
Ask them, "How tall is the tree?""How did the first problem help you with the second problem?"
Data & Statistics:
Representing and analyzing data allows us to notice and wonder about relationships.
Data & Statistics:
Representing and analyzing data allows us to notice and wonder about relationships.
CONNECTING GRAPHS AND CONTEXTS
Think with curiosity and wonder when exploring problems
Connect mathematical concepts with other areas and interests
Establish a "Graph of the Week" routine.
Share an infographic that is both contextually and mathematically interesting with your students.
Turner's Graph of the Week is an excellent resource for this and the source of our choice: 4/6 A Day In the Life of a US Teen
Ask "What do you notice? What do you wonder? What's going on in this graphic? What story does this graph tell?"
Additional questions prompts appear on the handout itself.
CRITIQUING AND CREATING GRAPHS
Use reasoning to analyze mathematical ideas
Explain and justify mathematical decisions
Circle graphs seem to be especially challenging for the media to create.
Share the following graphs with your students. Ask:
What's wrong with this graph?
Is a circle graph appropriate for this data? Why or why not?
What suggestions would you make to the person who made this graph? Can you fix it?
(There are plenty of COVID-19 related misleading graphs out there right now. Some students may be very interested in discussing them. Others may not. Please be sensitive to this and use your discretion.)
CENTRAL TENDENCY
Estimate reasonably
Explain and justify mathematical ideas and decisions
Ask your students to observe these 3 sets of data:
{1, 1, 3, 3, 4, 6, 6, 6, 6}
{1, 1, 1, 2, 3, 3, 8, 8, 9}
{1, 1, 3, 3, 3, 4, 6, 7, 8}
Ask:
How do they compare in terms of mean, median, and mode? Estimate first before calculating.
Which is the best measure of central tendency for each (mean, median, or mode)?
CENTRAL TENDENCY
Develop, demonstrate, and apply mathematical understanding through problem solving
Reflect on mathematical thinking
Have students choose a few of the problems on the right.
Invite students to reflect on their thinking by responding to questions such as:
What strategies did you use?
What decisions or changes did you have to make as you worked to solve the problem?
What was the most challenging part of the task? Why?
Can you find sets of positive integers that satisfy the following?
Three numbers with mean 3 and mode 2
Three numbers with mean 7 and mode 10
Three numbers with mean 8, median 10, and range 8
Four numbers with mean 7.5, mode 6, and median 7
Four numbers with mean 6, median 6.5, and range 11
Five numbers with mean 4, mode 3, and range 9
Five numbers with mean 4, mode 2, and range 6 (two possible solutions)
Five numbers with mean 7, mode 7, and range 10 (three possible solutions)
Source: https://nrich.maths.org/10995
CENTRAL TENDENCY: Choosing Measures
Explain and justify mathematical decisions
Apply conceptual understanding of mathematical ideas
Present the following scenario to your students:
An app developer has created three different apps. Apps are rated on a scale from one to five stars. Each app receives a rating from seven customers. This data is represented on the right.
Ask:
What is the mean, median, and mode of each set of data?
Which of these measures is the best summary of App 1? App 2? App 3? Explain your thinking.
If you had to use just one measure of central tendency and apply it to every app on the store, which would you choose? Defend your decision.
Financial Literacy: Gross & Net Pay
Financial Literacy: Gross & Net Pay
GROSS PAY
Explain and justify mathematical decisions
Task 1:
Would you rather…
(A) Earn an annual salary of $30 000, or
(B) Work full-time earning $15/hour?
Why? Justify your decision.
What assumptions are you making?
(Adapted from www.wouldyourathermath.com.)
Task 2:
Would you rather…
(A) Be paid $1000 per month plus 3% commission on sales, or
(B) Earn 5% commission on sales but not be paid a base salary?
Why? Defend your decision.
What assumptions are you making? When would the other option be a better choice?
Please see the related WYR…? Numeracy Task on the Secondary Homepage.
GROSS PAY WITH OVERTIME
Apply mathematical understanding through problem solving
Connect mathematical concepts to personal interests
Provide a selection of problems involving gross pay with overtime. Some ideas are below. For all problems, assume the BC standard of overtime which is time-and-a-half for hours worked over 40 hours in a week.
What is the gross pay if someone works 48 hours one week and makes $16/hr?
What is the gross pay each week if someone works 36 hours one week and 45 hours the next week. They make $17/hr.
Who had the higher gross pay this week, someone who worked 40 hours at $25/hr or 46 hours at $21/hr? Which job would you rather have? Why?
Someone makes $22/hr. How many hours did they work one week if their gross pay was $1078?
What is someone's hourly wage if they worked 50 hours and their gross pay was $1017.50?
Write a scenario involving gross pay with overtime (ie. hourly wage and number of hours worked) that results in $1000 gross pay for one week.
NET PAY
Apply mathematical understanding through problem solving
Connect mathematical concepts to personal interests
Tell students to use the chart on the right to calculate the gross pay and net pay for one week if one earns:
$26/hr and works 36 hours that week
$500/week and 6% commission on $12 000 sales that week
If the second person worked 40 hours that week, how much did they earn per hour on average?
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