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If units are related, you can use that relationship to predict “how many” of one unit, if you know “how many” of the other.
If you use a bigger unit, you need fewer of them
Proportional reasoning is about unitizing, grouping it, counting the groups and thinking of comparisons multiplicatively.
B2.9 represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts
Think of comparisons multiplicatively
Understand that if units are related you can use that relationship to predict “how many” of one unit, if you know “how many” of the other.
I can make predictions to calculate rates and ratios
I can think of comparisons multiplicatively
Cuisinaire rods
Multiplicative thinking is indicated by a capacity to work flexibly with the concepts, strategies and representations of multiplication (and division) as they occur in a wide range of context
Cuisinaire Rod Tasks to encourage proportional reasoning:
What single colour rods make a line as long as 4 orange rods?
A line of 8 one colour rods matches a line of 5 of another colour rid. What rods could you use?
A light green cuisinaire rod is worth 9 (or 15). What should the other rods be worth?
Using “The 5 Pratices of Math Discourse” https://www.curriculumassociates.com/blog/five-ways-to-promote-math-discourse
Consolidate the “Rates for internet” task.
SEL Self-Assessments (English) and Teacher Rubric
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