On Similar Triangles

By Ashli Black

The fact that a line has a well-defined slope—that the ratio between the rise and run for any two points on the line is always the same—depends on similar triangles.
(p.12, 6–8 Progression on Expressions and Equations)

As students are building their understanding of dilation at the beginning of grade 8 in Unit 2 of the LearnZillion Illustrative Mathematics 6–8 Math curriculum, an activity asks students to dilate different quadrilaterals using a given center and dilation factor on a square grid. Here are the results of two of the dilations in that activity involving triangles: Continue reading “On Similar Triangles”

NCSM and NCTM 2018 Roundup

It was great to see so many of you at NCSM and NCTM. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below.

We enjoyed the conversations we had with those of you that are using the IM 6–8 Math curriculum and are looking forward to High School and Elementary.

Check out some photos and all of the IM presentations below, including Bill McCallum’s The Promise of Open Curriculum.

Which presentations did you attend and which was your favorite? Continue reading “NCSM and NCTM 2018 Roundup”

What is an instructional routine?

By William McCallum and Kate Nowak

People use routines for all kinds of things. Routines give structure to time and interactions. People like structure. When a child comes home from school, there might be a routine. She expects a snack, homework time, play time, dinner, some television, a bath, pajamas, a book, and to get tucked into bed. She might have responsibilities, like setting the table for dinner, and engage in predictable dialog along the way, like sharing something that happened at school. She might expect her father to sing her a song. (Over and over and over again, in the case of my daughters—Bill.) The routine makes her comfortable and makes necessary chores go smoothly. Continue reading “What is an instructional routine?”

Sometimes the Real World Is Overrated: The Joy of Silly Applications

By Charles Larrieu Casias

One of the cool things about math is that it can provide powerful new ways of seeing the world. Just for fun, I want you to open up this lesson from the grade 8 student text. Take a quick skim. What do you notice? What do you wonder?

When writing this lesson, I was guided by a few key questions:

  1. To paraphrase Dan Meyer: If I want arithmetic with scientific notation to be the aspirin, then how do I create the headache?
  2. What are some weird, silly comparisons involving really large numbers?
  3. Here, towards the end of 8th grade, what should students be doing to transition towards the high school mathematical modeling cycle?

Continue reading “Sometimes the Real World Is Overrated: The Joy of Silly Applications”

Instructional Materials Matter: Interpreting Remainders in Division

By Jody Guarino

We know instructional materials play a key role in student learning experiences but how do we ensure our students are learning from coherent high-quality instructional materials that engage them in critical thinking and provide opportunities to “do math?”

Let’s think about this from the lens of a 4th grade standard, 4.OA.A3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing in for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Continue reading “Instructional Materials Matter: Interpreting Remainders in Division”

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