Common Core Algebra Preparation

Arithmetic Review

1. Arithmetic on a Grid: Counting unit squares. Sum, difference, product, quotient.
2. Two-Digit Addition: Two-digit numbers shown as $a(10)+b$ on grid. Addition with regrouping, carrying.
   Exercises: addition
3. Two-Digit Subtraction and Multiplication: Subtraction with borrowing, multiplication with regrouping.
   Exercises: subtraction, multiplication, division
4. Negative Numbers: Green squares have value $+1$, pink squares have value $-1$. Sums and differences. Word problems involving debt.
   Exercises: addition, subtraction
5. Multiplication and Division with Negative Numbers: Products and quotients with negative numbers on the grid, introduced through analogy and pattern-matching.
   Exercises: multiplication, division
6. Fraction Addition and Subtraction: Visualizing fractions using pie slices. Reducing to lowest terms. Finding common denominators.
   Exercises: addition, subtraction
7. Fraction Multiplication and Division: Using an expanded grid to visualize fractions.
   Exercises: multiplication, division
8. Arithmetic Test

Variables, Expressions, and Simple Equations

1. Variables and Expressions: Expressions as quantities. Simple linear expressions. Sliders for variables.
   Exercises: evaluation 6.EE.2
2. Word Problems: Cost of $n$ items. Multi-variable expressions.
   Exercises: expressions 6.EE.6, A.SSE.1a, A.CED.2
3. More Complicated Expressions: Examples involving negative numbers, division, fractions.
   Exercises: evaluation, division A.SSE.1a
4. Equations as Sentences: Solving equations by trial and error, or by sliding a slider. Inverse problems as word problems.
   Exercises: solving 6.EE.5, A.CED.1
5. Grouping in Addition and Subtraction Problems: Parentheses, associative law of addition, order of operations for addition and subtraction. Simplifying expressions using the associativity of addition to regroup, including for subtraction.
   Exercises: evaluation, simplifying 6.EE.3, A.APR.1
6. Solving $x+b=c$: Adding a constant to both sides.
   Exercises: solving 6.EE.7, A.REI.1, A.REI.3
7. Grouping in Multiplication Problems: Order of operations including multiplication. Multiplying three numbers, associative law of multiplication and its use in simplifying expressions.
   Exercises: evaluation 1, evaluation 2, multiplication, division 6.EE.3, A.APR.1
8. Solving $ax+b=c$: Adding $-b$ and then multiplying by $$1/a$$, or dividing by $a$.
   Exercises: solving 1, solving 2 6.EE.7, A.REI.1, A.REI.3
9. Applications of Linear Equations: Balanced scale, budgeting, temperature conversion.
   Exercises: solving 6.EE.7, 7.EE.4a, A.CED.1, F.BF.1a
10. Variables, Expressions, and Simple Equations Test 1
11. The Distributive Law and Combining Like Terms: Expanding $a(x+c)$, $a(bx+c)$, $-(bx+c)$. Simplifying $ax+bx$ to $[a+b]x$.
    Exercises: simplifying 1, simplifying 2, combining like terms 6.EE.3, A.APR.1
12. Manipulating Linear Expressions: Adding, subtracting, scaling, simplifying. Commutativity of addition and multiplication. Zero and one laws.
    Exercises: simplifying 1, simplifying 2 6.EE.3, 7.EE.1, A.APR.1
13. Solving $ax+b=cx+d$: Adding $-cx-b$ to both sides.
    Exercises: solving 8.EE.7b, A.REI.1, A.REI.3
14. Variables, Expressions, and Simple Equations Test 2

Linear Graphs

1. Points and Coordinates: Connecting the ordered pair $(x, y)$ with the coordinate plane. Quadrants.
   Exercises: quadrants, coordinates 6.NS.6bc
2. Investigating $y=x+b$: Finding the $y$-intercept $(0, b)$ of a line.
   Exercises: $y$-intercepts F.IF.7a, F.BF.3
3. Investigating $y=mx$: Lines with slope $m$, positive or negative.
   Exercises: slopes 8.EE.5, 8.F.2, F.LE.1a
4. Investigating $y=mx+b$: Slope and $y$-intercept.
   Exercises: $y$-intercepts 1, slopes 1, $y$-intercepts 2, slopes 2, equations 8.F.3, F.IF.7a, F.LE.1a
5. Solving Equations Graphically: Graphing each side and finding the intersection, e.g. for $ax+b=cx+d$.
   Exercises: solving A.REI.11
6. Finding Formulas for Approximately Linear Data: Simple statistics application. Uses root-mean-square error informally. 8.SP.2, F.IF.4, S.ID.6ac
7. Slopes, Rates of Change, and Similar Triangles: Calculating the slope of a line from any two points on it. Derivation of the equation $y=mx$ or $y=mx+b$ from a line’s slope and $y$-intercept.
   Exercises: computing slopes 8.F.4, F.IF.6, F.LE.1b, F.LE.2
8. Finding Equations for Lines: Point-slope form.
   Exercises: point-slope form F.LE.2
9. Parallel and Perpendicular Lines: Slopes $m$ and $$-1/m$$.
   Exercises: parallel lines, perpendicular lines 8.EE.8c
10. Equations for Lines in Standard Form: $Ax + By = C$. Converting to slope-intercept form. Computing slopes, $x$- and $y$-intercepts.
    Exercises: converting to slope-intercept form, $y$-intercepts, $x$-intercepts A.CED.4, A.REI.10
11. Linear Graphs Test

Descriptive Statistics

1. Summarizing a Collection of Measurements: Converting to common units. Dot (line) plots. Median and mean. Histograms.
   Exercises: median from a list, median from frequencies, mean 6.SP.3, 6.SP.4, N.Q.1, N.Q.2, N.Q.3, S.ID.1, S.ID.2
2. Box Plots: First and third quartiles, interquartile range. Comparing data collections.
   Exercises: quartiles, box plots 6.SP.4, S.ID.1, S.ID.2, S.ID.3
3. Descriptive Statistics Preparation Test

Systems of Linear Equations

1. Solving Systems of Linear Equations by Graphing: Solutions are intersections of graphs.
   Exercises: checking, solving 8.EE.8a, A.REI.6
2. Solving Systems of Linear Equations by Subtraction: Solving for a difference equal to 0.
   Exercises: solving 8.EE.8b, A.REI.5, A.REI.6
3. Systems of Linear Equations Preparation Test