Outcome #1
Working with Numbers
Embedded Files
Description
This outcome covers the following:
understanding integers and integer operations
fractions (beginning with unit fractions)
proportional reasoning, including unit rates, percents and solving proportions (including unit conversions)
Curriculum Expectations: B1.1, B1.2, B1.3, B3.1, B3.2, B3.3, B3.4, B3.5, E1.3
Notes:
this outcome includes E1.3 Measurement Systems and Conversions - conversion ratios should be provided to students when necessary
Specific expectations B1.2 (number sets) and B1.3 (density, infinity etc.) are not formally assessed, but may fit well into concepts in this Outcome
Relating integer values to direction and location will be taught throughout outcomes 5 and 6
Emerging
Emerging
I can evaluate simple expressions involving integers and order of operations.
I understand and can use unit fractions to determine other fractional amounts.
Notes/Examples:
Evaluate expressions such as:
Using our understanding of a unit fraction like 1/6 to determine what 5/6 of 72 would be
Developing
Developing
I can determine an unknown between and within simple ratios.
I can move between fractions, decimals and percents.
Notes/Examples:
Find the missing values in each proportions, written in both fraction form and ratio form (focus on noticing the scale factor between and within each proportion)
Proficient
Proficient
I can make comparisons using unit rates and proportional reasoning.
I can solve problems which include operations with positive and negative fractions and mixed fractions.
Notes/Examples:
Comparing two products: which is the better buy.
Turning a word problem into ratios to solve for an unknown portion.
Exceeding
Exceeding
I can solve problems involving rates, percentages, and proportions in various contexts.
Notes/Examples:
Problems should require multiple steps.
Measurement Conversions are included here (linking to Measurement Outcome).
Eg. a) Convert 30 in to cm. b) Convert 62 lbs to kg.
Extending
Extending
I can consistently solve multistep problems involving proportional reasoning in various contexts.
Notes/Examples:
Consider linking this level to other outcomes in the course.
Questions should require deep understanding of the outcome and may require multiple steps to solve.
Sample Assessments
(Approaching Standard)
(Approaching Standard)
(Reaching Standard)
(Reaching Standard)
(Reaching Standard -> Extending Understanding)
(Reaching Standard -> Extending Understanding)
Lesson Ideas
These activities (including number strings) should only take 5 - 10 minutes at the start (or anytime) of class. They are designed to help students work on their calculation skills with concepts such as: multiplying, dividing, integers and fractions.
Working with Unit Fractions
Working with Unit Fractions
This lesson makes use of Unit Fractions to help rethink how we teach a fraction of a number.
It leads well into the Percent Trees lesson.
Percent Trees
Percent Trees
After learning how to use unit fractions, this lesson helps solidify the concept of a unit fraction. In this case: 1% = 1/100
Check Your Understanding Questions
Nice number puzzle for a warm up activity.
Helps with multiplication and addition of positive numbers.
A video by Howie Hua
What happens if we added fractions straight across? We get an interesting result!
In this activity students will design their own unit of measurement.
They will choose a name, use their new unit to convert distances and finally create their own measurement tool.
This is a short game to play with your class. It is a good opportunity to discuss number sets.
You can record your results and then access the collection of results for use in the Data Outcome.
Questions from this site could be used for warm up activity or to build a lesson around.
This problem allows students to explore order of operations.
Extension: Can you represent all numbers from 1 - 100.
Hint: Consider using 4! 0.4 etc.
A&W 3/9 Burger
A&W 3/9 Burger
A failed marketing attempt in the 1980's to turn customers away from the McDonald's 1/4 Pounder, A&W introduced the 1/3 Burger.
But it turns out, people struggled with the math, and thought the burger was smaller!
The video is fantastic!
This tweet was shared during an MSNBC discussion. It highlights how easily numbers can be misunderstood.
(This one is definitely worth a watch)
In this VNPS lesson, the students will work through two multi-step tasks using various proportions.
These proportion questions involve various topics (unit rates, conversions, multi-step problems) for reached, exceeded and mastery. Suggested to be used in passed two after all concepts of Outcome 1 have been taught. Final answers are given on the last page.
This Thinking Classroom activity allows students to practice basic arithmetic skills while also using logic skills to help solve these puzzles.
A comparison of Lego Star Wars and Lego Friends. Looking at the unit rates, then finding comparisons by graphing. Adapted from Is Lego Gender Bias from mrorr-isageek.com
Here is an activity that was adapted from the CEMC website. It combines finding areas and adding fractions.
Coding Activities
Using Code: Ratio Reducer
Using Code: Ratio Reducer
This program asks the user to enter a ratio and then reduces it to lowest terms.
Note: This would be a more challenging program for students to create on their own.
Desmos Classroom Activities
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