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.
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Week 10 – More on Ratios
Representing Equivalent Ratios with Tables
LEARNING GOALS
— 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?
LEARNING GOALS
— 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.
Week 9
Area of Irregular Shapes
CCSS.MATH.CONTENT.6.G.A.1
Find the area of polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld 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
Week 8 Equivalent Ratios
Creating Double Number Lines to Find Equivalent Ratios
 Draw and label a double number line diagram from scratch, with parallel lines and equallyspaced 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
Week 6 – Ratio
Ratios and Ratio Language
 Comprehend the word “ratio” (in written and spoken language) and the notation (in written language) to refer to an association between quantities.
 Describe (orally and in writing) associations between quantities using the language “For every of these, there are of those” and “The ratio of these to those is a:b (or a to b).”
 Draw and label discrete diagrams to represent situations involving ratios.
Student interpretations of a 1:2 ratio:
Area of Irregular Shapes
CCSS.MATH.CONTENT.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes
Week 3 – Parallelograms
Finding Area of Parallelograms by Decomposing and Rearranging
Learning Goals 

