https://padlet.com/sethwillbe/kxxgu760rzokbtxx Common exponent misconceptions and action plan for correction. en-us 2023-10-15 19:05:49 UTC 2023-10-15 21:07:34 UTC hello@padlet.com sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747010553 Most students learn about exponents in the 6th grade, and they are often taught it as repeated multiplication. Unfortunately, learning the concept in this way can cause students to look at a problem like 7^2 and think of it as 7 x 2 = 14. Instead, students who learn about exponents in a geometric way by starting from squaring and cubing understand the relationship between a base and a power more completely than students who learn through repeated multiplication.]]> 2023-10-15 19:20:11 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747010553 sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747020063 Ask students about what they know about squares. Discuss the relationship between the side lengths, and talk about the area of a square. Then, ask the students if they have heard about the phrase "squaring a number" and what that could possibly mean. Have students work with a partner to discuss the idea of squaring a number.

Present the problem "7 squared" and have students come up with ways to evaluate this. Student solutions will most likely be encompassed with 7 x 2, 7 x 7, or a seven-by-seven sided square.]]> 2023-10-15 19:35:28 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747020063 sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747043026 FACT: Agree/Disagree - students will look at a set of statements and decide whether they agree or disagree with each statement. Then, they will give their reasons for each choice. 

Draw a 7 by 2 rectangle, a 7 by 7 square, 7 x 2, and 7 x 7 on the whiteboard. Have students write on their own paper whether they agree or disagree with each representation of 7 squared, and why they agree/disagree with each representation.]]> 2023-10-15 20:11:18 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747043026 sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747048780 FACT: Think Pair Share - students begin by thinking individually about a posed problem, and then they pair up to discuss their ideas with their partner. Once discussion is done, each pair of students shares their answer in a classroom discussion. 

Students will have done the "Think" step of Think Pair Share in the Agree/Disagree exercise. Have students pair up and share their reasoning for each representation of 7 squared and why they agreed or disagreed with each one. ]]> 2023-10-15 20:20:12 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747048780 sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747053184 Once each pair of students is done sharing their ideas, have each pair talk about why they either agreed or disagreed with each representation. Guide student discourse by asking how each representation relates to the other, focusing on the connection between the geometric and algebraic representation of squaring. Students should observe the difference between the 7 by 2 sided rectangle and the 7 by 7 sided square, and the connection between each of those shapes with 7 x 2 and 7 x 7. ]]> 2023-10-15 20:27:43 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747053184 sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747064783 Give students square blocks to practice squaring each number geometrically. Have students square 1 through 6 and calculate the area of each shape. Then, have students record any patterns they see as they square each increasing number. 

Once students are comfortable with squaring, ask them to use their models to attempt to cube each number. Have students discuss the properties of cubes and have them use manipulatives to visualize the process of cubing. ]]> 2023-10-15 20:47:24 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747064783 sethwillbe https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747074841 Once students have made their squares and cubes of 1 - 6, discuss with the class the connection between the geometric representations and the algebraic way of solving exponents. Discuss the relationship between area and squaring and volume and cubing, and ask students how they could solve higher order exponents. 

Exit Ticket: Ask students about whether their initial understanding of exponents was altered by the geometric activities, and have them write down any confusion with the idea of exponents. ]]> 2023-10-15 21:07:34 UTC https://padlet.com/sethwillbe/kxxgu760rzokbtxx/wish/2747074841