Math 350, S07 - Review Guide for In-Class “Partial” Exam III
Addition & Subtraction
Mental Addition / Subtraction Strategies: You should be able to use mental
strategies to solve multi-digit addition / subtraction problems: You should be able to
write down notation that clearly illustrates the thinking you used to do the addition /
subtraction in your head. You should be able to do any problem using two or more
significantly different strategies. In particular, you should be familiar with and able to
use any of the following strategies: break apart a number, compatible / friendly
numbers, left-to-right, compensation, make ten (addition only), add-up (subtraction
only)
-Alternative Algorithms:
Addition: You should know / be able to use in any base, and clearly / neatly
diagram with base blocks the following algorithms: partial sums, left-to-right
Subtraction: You should know / be able to use in any base, and clearly / neatly
diagram with base blocks the following algorithms: left-to-right,
Other Alternative Algorithms: You should know / be able to use, and explain any of
the other alternative algorithms discussed in class or covered on a homework
assignment.
Multiplication:
- Know the four different types of multiplication; be able to write “real-life” word
problems for each type; be able to draw appropriate diagrams for each type.
Remember, the order of the multiplication matters! 2 x 3 has a different
meaning than 3 x 2. Also, for repeated addition, you should be able to draw
both set models and length-measurement number line models. (see in-class
activity and HW #18)
- Be able to solve problems involving the Cartesian product interpretation of
multiplication (see HW #18)
- Be able to model multi-digit multiplication problems using base 10 blocks You
should be able to do this using two approaches: multiplication as repeated
addition, and the rectangular area model for multiplication (this one is
particularly good for modeling two-digit number X two-digit number) (see
class notes and HW #18, HW #19)
- Be able to multiply multi-digit numbers using: i) the partial products algorithm;
ii) the standard algorithm; and iii) using the distributive property and breaking
apart place values. For all of these, you should be able to make and describe
connections to the rectangular area model for multiplication involving base 10
blocks. (see class notes and HW #18, HW #19)
- Be able to use the lattice algorithm to multiply multi-digit numbers (HW #19)
- Know multiplication terminology: factor, product
Properties of Whole Number Arithmetic
- Know the various properties for whole number arithmetic. This involves
knowing the terminology, being able to recognize when a particular property
is being used, being able to provide examples of the properties, knowing
when the properties do and do NOT apply, and being able to model the
properties using either a set model or a length-measurement number line
model. (See class notes, HW #18, HW #19)
