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Review Guide for Exam 3 - Mathematic Elementary Techniques I | MATH 350, Exams of Mathematics

Material Type: Exam; Class: Topics in Math Elem Tch I; Subject: Mathematics - MATH; University: Texas A & M University-Commerce; Term: Unknown 1989;

Typology: Exams

Pre 2010

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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)
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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)

Division

  • Know the two different types of division: measurement and partitive. Be able to write “real-life” word problems for both types and be able to recognize whether a word problem involves measurement division or partitive division. Be able to model both types of division with a set model picture, and be able to model measurement division with a length-measurement number line model. Also, be able to connect both types of division to their appropriate missing factor multiplication statements. This is very important. Make sure that you have these two types of division solidly straight in your mind. (see class notes, HW #20)
  • Be able to rewrite division statements as multiplication statements and vice versa. (see class notes and HW #20)
  • Know the three different situations involving division with zero and be able to explain why the answer is what it is in each of the situations. (HINT: Rewriting the division problems as missing factor multiplication problems is very helpful in the explanations.) (see class notes and HW #20)
  • Understand the different ways that a remainder can be handled in real-life situations. Be able to write “real-life” word problems that lead to handling the remainder in all of the different ways. (See Dealing with Remainders activity and HW #20)
  • Know division terminology: dividend, divisor, quotient, remainder
  • Be able to do multi-digit division using both the scaffolding algorithm and the standard long division algorithm. For the scaffolding algorithm, you should be able to do it using “easy” multiplication facts that one could expect any third grader to know. (see Introduction to Division Algorithms Problems, class notes and HW #21)
  • Be able to model and make connections to the standard long division algorithm using base 10 blocks and the partitive interpretation of division when the divisor is a single-digit number. (see Introduction to Division Algorithms Problems, class notes and HW #21)