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

Students reviewed the important concepts from our recent investigations, and determined a formula for the area of ANY parallelogram using the base and the height.

Students drew diagrams to show that the area of a triangle is half the area of an associated parallelogram.

Students determined a formula to find the area of ANY triangle.

Comprehend the terms “base” and “height” to refer to one side of a parallelogram and the perpendicular distance between that side and the opposite side.

Generalize a process for finding the area of a parallelogram, using the length of a base and the corresponding height.

I am so excited to work with these amazing students! We began by watching a video from Stanford Mathematics professor Jo Boaler, focusing on 4 really important messages that we will be reinforcing throughout the year.

After we discussed the video, we talked a bit about the difference between a fixed mindset and a growth mindset, and students did a self-assessment as to their mindset.

FIXED MINDSET: Assumes intelligence and other qualities, abilities, and talents are fixed traits that cannot be significantly developed.

GROWTH MINDSET: Assumes intellligence and other qualities, abilities and talents can be developed with effort, learning and dedication over time.

On Wednesday, we started with Which One Doesn’t Belong? WODB activities help students to develop reasoning skills, make logical arguments, express their ideas in words, and engage with visual mathematics—which ultimately leads to deeper and more meaningful understanding of challenging topics and concepts.

computation

number sense

reading graphs

problem solving

patterns and sequences

date analysis and probability

spatial reasoning

fractions

algebra and functions

geometry

Together, students worked on the Four 4’s task. For students, this is a very safe and non threatening activity. It builds number sense and is a fun challenge. This task is also a really nice way of helping them become comfortable sharing their work in front of the class.

On Friday, students discovered that they could not seem to complete the Four 4’s task. I showed them factorial (!) which is very helpful for 11 and 13. We had some WWDB? discussions and completed Minute 2. Next up, tiling the plane.