CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.
This course teaches simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications are drawn from the physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis is on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world.
Play with objects on a teeter totter to learn about balance. Test what you've learned by trying the Balance Challenge game.
Students will use ratios to demonstrate the connections between proportional relationships, lines, and linear equations. Students will solve problems using a cooperative, kinesthetic activity in which they will create a ratio table, then graph proportional relationships with their bodies to demonstrate that the ratio (or rate) is the slope that will always pass through the origin.
Students often think additively rather than multiplicatively. For example, if you present the scenario, "One puppy grew from 5 pounds to 10 pound. Another puppy grew from 100 pounds to 108 pounds." and ask, "Which puppy grew more?" someone who is thinking additively will say that the one who now weighs 108 grew more because he gained 8 pounds while the other gained 5 pounds. Someone who is thinking multiplicatively will say that the one that now weighs 10 pounds grew more because he doubled his weight while the other only added a few pounds. While both are correct answers, multiplicative thinking is needed for proportional reasoning. If your students are thinking additively, you can nudge them toward multiplicative thinking with this activity.
Students will analyze ratios and use proportions to solve problems using a cooperative, kinesthetic activity in which they will create “human ratios.” Students will apply proportional reasoning to demonstrate application of a multiplicative situation by using cross products to solving proportions.
Students will analyze ratios and use proportions to solve problems using a cooperative, kinesthetic activity in which they will create “human ratios.” Students will use ratios to compare two quantities, then solve problems cooperatively by demonstrating how proportions are written to show equivalent ratios.