Overview for Exam 2
Included is a list of main topics you should know for the exam. To see how these might be asked, study your class notes and review your HW problems.
· Addition Algorithms/Approaches: Know the concrete model of carrying with manipulatives, left-to-right and right-to-left (using thousands, hundreds, tens and ones grouped in the right position and adding), the lattice algorithm and scratch algorithm.
· Subtraction Algorithms: Know how to borrow using manupulatives (turning a flat into ten longs, a long into ten units, etc.) and the equal-additions algorithm.
· Other bases: Be able to add and subtract using the above methods in different number bases as well.
· Multiplication Algorithms/Approaches: Know that times means repeated addition, understand the array/area models, know what the Cartesian product of two sets is and its connection to multiplication (using the fundamental counting principle), know how to use and be able to identify by name the properties of multiplication of whole numbers (from p. 147 – though remember we gave a stronger form for the zero multiplication property, that ab = 0 implies that a = 0 or b = 0) as well as the distributive properties of multiplication over addition and subtraction (p. 148) and how to show using area models.
· Division Algorithms/Approaches: Know the set/partition model, the missing factor model, and the repeated subtraction model. Understand why these imply division by 1 results in the same number and division by 0 is not allowed.
· Understand the division algorithm and what is meant by the connection between a/b and quotient q and remainder r in a = bq + r.
· Multiplication Algorithms: A single-digit number multiplied by a several-digit number can be carried out using multiplication by 10n and the distributive property, two-digit number multiplication by using place values and zeros to represent missing place values, understand and be able to use the lattice algorithm for multiplication.
· Division Approaches: Repeated subtraction toward short division involving carrying, standard long division by a two-digit number
· As both multiplication and division are represented by powers or exponents, know basic properties we discussed in class of exponents (as in HW A: #5 and B: #4-5).
· Follow the summary of this section we did in class today for mental mathematics.
· Estimation of Sums/Differences: Front-end w/adjustment means doing biggest place-value digits first then adjusting at the next place value, grouping and clustering when multiple numbers are added together, then rounding for either addition or subtraction.
· Estimation of Products/Quotients: Front-end for multiplication and compatible numbers for division
Be able to write expressions with variables for several different settings and patterns as per our class notes and assigned homework