Author: gilliangiles

Solving for Areas 7.G.A

gilliangiles CCSS-Math Learning Progressions

This learning progression is based on the concepts of area. There are three math tasks the students will need to perform: an entry task related to a real world problem, a walk around activity, and an exit task related to the entry task. The walk around activity involves the entire class getting up and moving around the room to solve problems posted on the walls. This is one way to get the students to stretch their legs while also keeping them actively engaged in the lesson. There will be twelve problems posted on the walls around the room and the students will choose eight to solve. The idea of having the students choose which problems to do gives them the sense of freedom within their own education. The CCSS-Math that align with this learning progression are as follows:

7.G.A.1 Geometry: Draw, construct, and describe geometrical figures and describe the relationship between them.

  • The students will be finding areas and demonstrating their knowledge of the different shapes used throughout the unit.

HSG-GPE.B.7 Expressing Geometric Properties with Equations: Use coordinates to prove simple geometric theorems algebraically.

  • During lesson 6.7, there will be a couple problems where the students need to use the distance formula to algebraically solve for one side of a shape in the coordinate plane.

HSG-SRT.B.4 Similarity, Right Triangles, & Trigonometry: Prove theorems involving similarity.

During the lesson about areas, 6.7, the students will need to use the Pythagorean Theorem to solve for the height of triangles.

Learning Progression

Geometry Learning Progression

gilliangiles CCSS-Math Learning Progressions

Learning Progression

The CCSS-Math cluster I used for this learning progression is

  • HSG-CO.A.1,
  • HSG-CO.A.2,
  • HSG-CO.A.3,
  • HSG-CO.A.4,
  • HSG-CO.A.5:  Congruence: Experiment with transformations in the plane.

The mathematical practices used are as follows:

  • MP1: Make sense of problems and
    persevere in solving them.
  • MP4: Model with mathematics.
  • MP5: Use appropriate tools strategically.

The tasks for this LP are as follows:

  • Task 1: physically modeling transformations in a group (MP1, MP5)
  • Task 2: modeling transformations using objects in a coordinate plane (MP4, MP5)
  • Task 3: review quiz about transformations on Kahoot (MP5)

I will elicit evidence from the following:

  • student discourse and syntax
  • assessment on the material
  • student participation and interactions with each other

Learning Progression

Pumpkin Pie Problem GMD.A

gilliangiles HS Geometry, Picture Problems

The Problem:

If I had a whole pumpkin pie with a diameter of 8 inches, and a height of 2 inches, what is the maximum amount of pie I could eat? Find the volume of the pie.

CCSS-Math:

HSG-GMD.A.3 Geometric Measurement and Dimension: explain volume formulas and use them to solve problems.

The relevance of this activity is that it can be used around Thanksgiving time, so the students have a real life example of how and when they could solve for the volume of a shallow cylinder. The teacher could have a couple different approaches for student engagement. He/she could have his/her students discuss in their groups what they think the solution is, the students could have this as an individual entry task, or there could simply be a class discussion of the process to solve this problem. All of those options could engage students in their current understanding of finding the volume of a cylinder, as well as allow the teacher to lead the lesson based off of the students’ findings. If the teacher wanted to take that extra step, he/she could potentially bring in an actual pumpkin pie for the students to reference (and possibly eat).

Bouncing Into Math CCSS.MATH.5.G.A.2

gilliangiles HS Geometry, HS Modeling, Technology Teaching Issues , ,

Some math teachers might ask the question “how can I adapt this curriculum to relate to real world scenarios?” One way to start is by taking an interest in what your students are interested in. There’s a time for lecture and there’s a time for, well, bouncing balls and having fun. This activity features measurement of a tennis ball bouncing and when it slows down, compared to a rubber ball bouncing and when it slows down, using the Ipad app called Video Physics. You might be asking yourself now “how in the world does this relate to the real world?” Well, once this activity is performed by questioning young minds, the students will want to know more. They’ll want to use the technology and math and relate it to people and if they were to keep jumping, at what point would those bounces become smaller and slower. This is an activity to get the students up out of their seats and “perform” mathematics in the classroom.

In this activity the students will need to get into groups of at least three and have an Ipad, a worksheet, a tennis ball, and a rubber ball. Each student will have his/her own job: recorder, video-taper, and ball bouncer. Each student will get to perform each task within the groups of three. The students will collect and record data pertaining to the tennis ball and the rubber ball and how each ball’s acceleration and height of the bounces differ slightly. Prior to the students gathering data, they will draw their prediction of what each ball’s graph will look like. This will give the students more insight to how the math aligns with reality. After they complete the worksheet given during this lesson, the class can discuss their findings as well as how else they could use this technology in their day to day lives.

This assignment relates to the Common Core State Standard

CCSS.MATH.5.G.A.2 Graph points on the coordinate plane to solve real-world and mathematical problems.

Bouncing Into Math Worksheet-1oj7bir