From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

Appendix

Implementing District Standards

Virginia is a not a Common Core State. We follow standards set by the state called the Virginia Standards of Learning (SOLs).  This unit was, in part, derived from an eighth grade standard that our district uses which is aligned to the SOL objective 8.15a-c which states that students will: .

1. a) Solve multi-step linear equations in one variable on one and two sides of the equation.
2. b) Solve two-step linear inequalities and graph the results on a number line.
3. c) Identify properties of operations used to solve an equation.

Taxonomies

The hyperlinks to the Common Core Math Taxonomies are listed below:

Addition/Subtraction: http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/

Multiplication/Division: http://www.corestandards.org/Math/Content/mathematics-glossary/Table-2/

Word Problems

One-Step Addition & Subtraction Problems (Tier 3 Reading Levels)

Examples of Change Plus (aka add to) & Change Minus (aka Take from) problems:

1. Alaysia had 3 blue fidget spinners.  On her birthday, Alaysia received 4 more blue fidget spinners.  How many blue spinners does Alaysia have?  (Change Plus; Result unknown) [3+4=?]
2. Alaysia had 6 blue fidget spinners.  She gave 2 spinners to her brother because he did not have any.  How many blue spinners does Alaysia have left? (Change Minus; Result Unknown) [6-2=?]
3. Alaysia had 3 blue fidget spinners.  She got some more blue spinners for making the honor roll.  Then Alaysia had 7 blue spinners.  How many blue spinners did Alaysia get for making the honor roll?  (Change Plus; Change Unknown) [3+?=7]
4. Alaysia had 6 blue fidget spinners.  She had 4 blue spinners left after giving her brother some blue spinners.  How many blue spinners did Alaysia give her brother? (Change Minus; Change Unknown) [6-?=4]
5. Alaysia had some blue fidget spinners.  She got 3 blue fidget spinners for her birthday.  Then Alaysia had 7 blue fidget spinners.  How many blue fidget spinners did she have before her birthday?  (Change Plus; Start Unknown) [?+3=7]
6. Alaysia had some blue fidget spinners.  She gave 2 blue spinners to her brother.  After that she had 4.  How many blue spinners did Alaysia have before? (Change Minus; Start Unknown) [?-2=4]

Examples of Compare More & Compare Less problems:

1. Alaysia has 4 blue fidget spinners.  Her brother, Malik, has 7 blue spinners.  How many more blue spinners does Malik have than Alaysia? (Compare More; Difference Unknown) [4+?=7]
2. Alaysia has 4 blue fidget spinners.  Malik has 7 blue spinners.  How many fewer blue spinners does Alaysia have than Malik?  (Compare Less; Difference Unknown) [7-4=?]
3. Alaysia has 4 blue fidget spinners.  Her brother, Malik, has 3 more blue fidget spinners than Alaysia.  How many blue spinners does Malik have?  (Compare More; Greater Unknown) [4+3=?]
4. Alaysia has 4 blue fidget spinners.  Her brother, Malik, has some blue fidget spinners as well.  Alaysia has 3 fewer spinners than Malik has.  How many blue spinners does Malik have? (Compare Less; Greater Unknown) [3+4=7]
5. Alaysia has some blue fidget spinners.  Her brother, Malik, has 7 blue spinners.  He has 3 more blue spinner than Alaysia.  How many blue spinners does Alaysia have? (Compare More; Fewer Unknown) [?+3=7]
6. Alaysia has some blue fidget spinners.  Her brother, Malik, has 7 blue spinners.  Alaysia has 3 fewer blue spinners than her brother.  How many blue spinners does Alaysia have?  (Compare Less; Fewer Unknown) [7-3=?]

Examples of Part-Part-Whole (Put together) problems:

1. Alaysia has some blue fidget spinners.  She keeps them on a shelf in her room and in her school locker.  On her shelf she has 3 blue fidget spinners.  In her school locker she has 4 blue fidget spinners.  How many blue spinners does Alaysia have? (Put together; Whole Unknown) [3+4=?]
2. Alaysia has 7 blue fidget spinners.  She keeps them on a shelf in her bedroom and in her school locker.  She has 3 blue spinners in her school locker.  How many blue spinners are on her bedroom shelf? (Put together; Part Unknown) [3+?=7, 7-3=?]

One-Step Multiplication & Division Problems (Tier 3 Reading Levels)

Examples of Equal Groups

1. Malik’s mother has 2 bags filled with 6 apples. How many apples does his mother have in all? (Equal Groups, Unknown Product) [2x6=?]
2. If Malik’s mother shares 18 apples equally among her 3 son’s, then how many apples will each son receive? (Equal Groups, Group Size Unknown) [3x?=18, and 18÷3=?]
3. If Malik’s mother has 18 apples to packed 6 to a bag, then how many bags are needed to pack the apples? (Equal Groups, Number of Groups Unknown) [?x6=18, and 18÷6=?]

Examples of Arrays/Area

1. Malik’s mother has a garden in her backyard. There are 2 rows of apples with 6 apples in each row. How many apples does his mother have in the garden? (Arrays/Area, Unknown Product) [2x6=?]
2. If Malik’s mother has 18 apples that arranged into 3 equal rows. How many apples are in each row of the garden? (Arrays/Area, Groups Size Unknown) [3x?=18, 18÷3=?]
3. If Malik’s mother has 18 apples that are placed into equal rows of 6 apples, then how many rows of apples are there in the garden? (Arrays/Area, Number of Groups Unknown) [?x6=18, and 18÷6=?]

Examples of Compare

1. Malik’s Spalding mini-basketball cost $6. He wants a Nike mini-basketball that cost 3 times as much as the Spalding basketball. How much does the Nike mini-basketball cost? (Compare, Unknown Product) [6x3=?]
2. Malik’s Nike mini-basketball cost $18 which is 3 times as much as the Spalding mini-basketball. How much does a Spalding min-basketball cost? (Compare, Groups Size Unknown) [3x?=18, 18÷3=?]
3. Malik’s Nike mini-basketball cost $18 and a Spalding mini-basketball cost $6. How many times as much does the Nike basketball cost as the Spalding basketball? (Compare, Number of Groups Unknown) [?x6=18, and 18÷6=?]