Today's estimation was the length of the Algebra I textbook when placed on top of the Steve Jobs biography. Students tended to underestimate this one. Some of them realized that the paper in the textbook would be thinner than the paper in the biography, so it would have more pages.
The class work started with a great questions, are 3 to the 5th power and 3 * 5 the same? Students were quick to point out that 3 to the fifth was 3 multiplied by itself 5 times. I made sure students contributed the academic vocabulary of the parts of a power number, the small number being called the power or exponent and the large number underneath it being the base number. If students didn't offer it already, I asked how these two expressions were related. A few realized that 3 times 5 was repeated addition while 3 to the 5th was repeated multiplication.
|Analyzing the differences.|
Productive struggle occurred in groups when it came to xy^2. Almost 3/4 of students thought it was xy*xy. Some students weren't convinced and had great conversations. I liked how a student said that xy is x times y so they can be singled out. Another student said that since the x doesn't have an exponent, any number without an exponent can have an exponent of 1. I made sure they shared their ideas to the whole class.
Then they worked on generalizing 20^51 * 20^12, and then analyzed a student mistake where they added the exponents even though they had different bases and multiplied the bases. They then worked on revisiting the commutative property of multiplication.
|The main source of productive struggle was the last problem and the 3rd to last problem.|
Another practice problem gave them a table of values. They saw the vertex and one x intercept. Students reasoned that since the x intercept was 2 and the vertex was (7,25), the highest point, then the other x intercept must be 5 away from the vertex at (12,0). They then repeated the same process to solve for a which was -1.
|Tile drawing and the algebra.|
|The virtual algebra tile representation.|
|Here you can see the extra tiles not needed to complete the square.|