## Description

- Overview:
- The intention of this curriculum guide is to provide teachers with supplemental materials to use to support students in strengthening their skills in various concept areas that are crucial for understanding beginning algebra. The activities are broken down by skill with links provided below. This is intended as a way to provide students with engaging, primarily computer-based activities to get extra practice with material that is covered elsewhere in the curriculum. This collection focuses on simulations and games using the computer—some resources may be ripe for teachers to develop unique activities to accompany the simulation and some possible suggestions are included with the descriptions. This series is intended to be pick-and-choose.

In this Curriculum Guide:

Activities and practice with: Integers, Exponents, Order of Operations, Distributive Property, Expressions, Equations and Basic Graphing

- Subject:
- Mathematics
- Level:
- Middle School, High School, Adult Education
- Grades:
- Grade 6
- Material Type:
- Activity/Lab, Diagram/Illustration, Game, Interactive, Simulation
- Author:
- Lee Gargagliano
- Date Added:
- 05/24/2018

- License:
- Creative Commons Attribution-NonCommercial-ShareAlike 4.0
- Language:
- English
- Media Format:
- Text/HTML

This curriculum guide has different kinds of resources, leaving the teacher with a wide range of choices.

This is a collection of resources targeting important conceptual foundations for Algebra. I'm remixing it with a few resources changed or added.

Integers:

The integers collection has several activities with number lines that help to ground the meaning of "negative" and understanding adding and subtracting integers, which is often misunderstood ("don't two negatives make a positive?" ... no, two 'wrongs' don't make a 'right' when adding.) The first is “flash” but includes how to do the activity with a counter and a number line.

The second is a geogebra exercise that includes reference to an “exit slip.” It’s OER so I “remixed” it to took that line out – that exercise is at https://www.geogebra.org/classic/WY5XRG87 .

I made an activity sheet for students to create a worksheet of their own here https://docs.google.com/document/d/19GnHdJQSKJ0Kttbu-2M9lJSz8SzzIaTXzrW449OmYWE/edit?usp=sharing

I also made a number line (from https://www.helpingwithmath.com/printables/others/NumberLineGenerator01.htm -- an open source site) and directions for playing the game in the first activity without a computer.

The exponents activities include a conceptual activity involving halving paper and then a review of more advanced rules. THey are broken down and explained well, though some students will need to proceed through the sequence more slowly to master each element.

For the Order of Operations I had to learn to find “Which Comes First and click it so it would load. It’s an excellent activity that focuses on determining which operation to complete and then does the calculation, so that calculation errors can't happen. It's also a Flash activity.

The “Geometric Proof of Distributive Property” failed to load for me through oercommons. I searched and found it on the Geogebra site here: https://www.geogebra.org/m/jUbGyhdq I think this activity would require a lot of explaining and supplementing for students to make the conceptual connection between the rectangle areas and the distributive property.

The “Area Model Algebra” from PhET has a much better visual design, showing the same concept. Students can click to see the different ways the idea would be expressed mathematically. I’d want some structured response sheets to make sure students were engaging in making those connections. This does an excellent job of starting with arithmetic concepts and showing how they connect with algebra visually and symbolically.

The activities for expressions are also excellent, with the PhET activity having clear visual design and options for displaying different aspects (numbers and/or variables, etc). I’d want to put together a sequence of questions to discuss w/ students and then structured response to make sure they’re engaging in the math concepts.

Regarding the “principles of equations and inequality,” the Khan Academy videos are pretty typical procedural explanations. Happily, it includes demonstrating with a number line how 7 – 11 is -4, and he explains what the first equation means. However, none of the more advanced questions get this level of review or conceptual grounding and include a fair amount of confusing terminology without explanation (e.g., “multiplicative inverse”). This lesson would be a good procedural review but could be frustrating for a student who doesn’t already understand the ideas behind “canceling out.”

I liked “What’s More” (but yes, had to hit “maximize”) for it’s low-stress logic, but would want to include activities to help students make the connections between the images and the math expressions that represent those relationships. The different levels make this adaptable.

The “pan balance” activity would, as noted, require teacher designed activities for students to know what to focus on and what represents what. I really like the suggestions for different activities in the lesson description.

I couldn’t figure out how to get the “Bermuda Triangle” exercise to work. I think if you get one wrong, then you have to go back to the menu to start over, but I’m not sure. This is also a Flash exercise with limited compatibility with different browsers and devices.

I liked the Geogebra lesson much better (Java based, not Flash), though it would also benefit from some pre-teaching. I work with students who guess and struggle with these without an explanation of how and why to get the intercept and then use the slope to find another point on the line.

This is a great collection!