This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller.
This lesson unit is intended to help teachers assess whether students are able to: identify when two quantities vary in direct proportion to each other; distinguish between direct proportion and other functional relationships; and solve proportionality problems using efficient methods.
This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.
This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.
This lesson unit is intended to help you assess how well students are able to manipulate and calculate with polynomials. In particular, it aims to identify and help students who have difficulties in: switching between visual and algebraic representations of polynomial expressions; and performing arithmetic operations on algebraic representations of polynomials, factorizing and expanding appropriately when it helps to make the operations easier.
This lesson unit is intended to help teachers assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.