Week 11 – Ratio Wrap Up

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.

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 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

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 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

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
  • Calculate the area of a region by decomposing it and rearranging the pieces, and explain (orally and in writing) the solution method.
  • Recognize and explain (orally) that if two figures can be placed one on top one other so that they match up exactly, they must have the same area.
  • Show that area is additive by composing polygons with a given area.