Students have been working hard on their understanding of ratios, and this week’s formative assessments indicate that they are ready to move on to Unit Rates and Percentages. They exhibit a solid understanding of representing ratios with diagrams and appropriate language, and they are confident in their ability to find equivalent ratios using diagrams, double number lines and tables. I am quite proud of their progress.
Representing Equivalent Ratios with Tables
— Comprehend the words “row” and “column” (in written and spoken language) as they are used to describe a table of equivalent ratios.
— Explain (orally and in writing) how to find a missing value in a table of equivalent ratios.
–Interpret a table of equivalent ratios that represents different sized batches of a recipe
These are just a few of the calculations that I observed as the students were generating tables of equivalent ratios.
How Much for One?
— Calculate equivalent ratios between prices and quantities and present the solution method (using words and other representations).
— Calculate unit price and express it using the word “per” (orally and in writing).
— Understand the phrase “at this rate” indicates that equivalent ratios are involved.
This problem is a review of students’ previous work on area and nets.
Area of Irregular Shapes
Find the area of polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Using Proportional Reasoning
This performance assessment task involves a range of mathematical practices from the standards, with emphasis on:
MP1:Make sense of problems and persevere in solving them
MP2:Reason abstractly and quantitatively
MP3:Construct viable arguments and critique the reasoning of others
MP4: Model with mathematics
MP5:Use appropriate tools strategically
MP6:Attend to precision
MP7:Look for and make use of structure
MP8:Look for and express regularity in repeated reasoning
Creating Double Number Lines to Find Equivalent Ratios
- Draw and label a double number line diagram from scratch, with parallel lines and equally-spaced tick marks.
- Use double number line diagrams to find a wider range of equivalent ratios.
Visual Representation of “8 is 32 times what number?”
- Making sense of multiplication and division
- Solving a problem with a visual representation