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Instructor: Anita Johnston        office: JM 250
phone: 517.796.8504    email: JohnstoAnitaM@jccmi.edu

MODELS, ALGORITHMS and PROPERTIES ASSIGNMENT...

Bring your Arithmetic Models, Algorithms and Properties Assignment (or a draft of it) to class each week.  For each item in Sections I and II you need to make up one example of your own that illustrates the topic.  This should not be an example taken from class notes or your text.

 

The final product should have a professional appearance.  Use technology (the computer, the internet, software programs, etc.) to find images to use for your examples.  The final product should be something you are “proud of” and can use as a resource in the future.  You will send it to me via email saved as a “rtf” file.  Please be sure the sections are in the appropriate order. 

 

I.  Models of Arithmetic:  This section should contain all of the models discussed for arithmetic processes.  For each model, write a word problem, draw the diagram, and write the associated equation.

 

a. Whole Number Arithmetic

                       i.    Addition – 2 models:  joining sets, joining lengths

                       ii.   Subtraction – 3 models:  take away, comparison, separation/missing addend

                       iii.   Multiplication – 5 models:  repeated addition, rectangular array, area, Cartesian product, tree diagram

                       iv.    Division – 3 models:  sharing/partition, missing-factor approach, repeated subtraction/measurement

 

b. Integer Arithmetic  (you need not write word problems for these)

                        i.   Addition – 3 models:  number line, colored counters/set, Algeblocks©

                        ii.  Subtraction – 2 models:  number line, colored counters,  2 concepts: take away, add the opposite, Algeblocks©

                        iii.  Multiplication – 3 models:  number line, colored counters, Algeblocks©

                        iv.   Division –  as inverse of multiplication, Algeblocks©

 

c. Fraction Arithmetic

                         i.   Addition – 2 models:  number line, area

                         ii.  Subtraction – 2 models:  number line, area

                         iii.  Multiplication – 2 models:  repeated addition, area  (use mixed numbers as needed)

                         iv.  Division – 2 models:  sharing/partition, repeated subtraction/measurement (use mixed numbers as needed)

                          v.  Converting Between Fractions and Mixed Numbers – area model

 

d. Decimal Arithmetic

                          i.   Modeling a decimal number – 1 model:  decimal squares

 

e. Ratio

                          i.   Three ways to interpret a ratio – give an example of each

 

II. Algorithms:  Give a fully worked out example problem illustrating each algorithm

 

a. Whole Numbers (add, subtract, multiply, divide)

                           i.   Expanded

                           ii.  Standard

 

b. Integers

                            i.  Standard “Rules”

 

c.  Fractions

                            i.  Add & Subtract:  Standard

                            ii. Multiply: Standard and Shortcut

                            iii. Divide: Standard and at least one other

                            iv.  Mixed Numbers:  one example of each operation; for addition and subtraction, chose problems that require regrouping and work your examples two ways (once in improper fraction form and once in mixed number form).

 

d. Decimals:  One example each for Add, Subtract, Multiply, Divide.  Work each example twice, using:

                              i.  Fraction method

                              ii. Standard method

 

e. Ratio and Proportion:  Write and solve one word problem three ways

                               i.  Informal Reasoning

                               ii.  Formal – 2 methods: equivalent fraction method, cross multiply method

 

f. Percent:  Write and solve one word problem two ways

                                i.  Equation Method

                                ii. Percent Scale (ratio and proportion) method

 

III.  Properties:  In this section you will need to include a copy of a complete properties of numbers grid, which we will be developing throughout the semester.

 

Properties Chart

  

Property	Whole Numbers	Integers	Rational Numbers
Closure
Identity Element
Commutative
Associative
Distributive
Additive Inverses
Zero
Multiplicative Inverse