1. 8th Grade STAAR Math: Tips & Strategies

2. The Real Number System π or √2 Rational Numbers Integers Whole Numbers
Any number that can be written as a ratio.
Includes perfect squares, terminating and repeating decimals.
Integers
Includes all whole numbers and their opposites (positive and negative).
Whole Numbers
All positive numbers and zero.
Irrational Numbers
All numbers that cannot be written as a ratio.
In decimal form, an irrational number does not terminate or repeat.
For example:
π or √2

4. Scientific Notation
A method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10, and a power of 10.
Positive Powers of 10
When you move the decimal to the left.
USE WHEN THE NUMBER IS GREATER THAN OR EQUAL TO 10.
Negative Powers of 10
When you move the decimal to the right.
USE WHEN THE NUMBER IS LESS THAN 1.

5. Proportions
A proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant.
k = y / x .
If “k” is the same every time, then the relationship is proportional.

6. Rate of Change/ Slope/ Unit Rate
A rate of change is a ratio of the amount of change in the output to the amount of change in the input.
The slope of a line:
the ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

7. Direct Variation
A direct variation is a relationship that can be written as
y = kx
“k” must be constant for there to be a direct variation.
If there is a direct variation, then we can say that
y varies directly to x

8. Linear Equations Linear equations can be written in the form
y = mx + b.
When b ≠ 0, the relationship between x and y is nonproportional.

9. Y-intercept
The y-intercept is the y-coordinate of the point where the graph intersects the y-axis.
The x-coordinate of this point is always 0.
The linear equation shown is written in the slope-intercept form of an equation.
y = mx + b
Its graph is a line with slope m and y- intercept b.
A linear relationship has a constant rate of change.

10. Graphing Linear Equations

11. Proportional vs. Nonproportional

12. Systems of Equations
A system of equations is a set of equations that have the same variables.
An ordered pair is a solution of a system of equations if it is a solution of every equation in the set.

13. Writing Linear Equations
Step #1:
Find the slope.
Using the formula, rise over run, or looking for key words (per).
Step #2:
Determine the y-intercept by looking at the graph, table, or word problem (initial value).

14. Bivariate Data
Bivariate data is a set of data that is made up of two paired variables.
If the relationship between the variables is linear, then the rate of change (slope) is constant.
If the graph shows a nonlinear relationship, then the rate of change varies between pairs of points.

15. Functions A function assigns exactly one output to each input.
The value that is put into a function is the input.
The result is the output.
A boy can only have one girlfriend
Not a function
Function

16. Parallel Lines cut by Transversal

17. Sum Angle Measures in Triangles
All three angles in a triangle add up to 180 degrees.

18. Remote Interior Angles
An interior angle of a triangle is formed by two sides of the triangle.
An exterior angle is formed by one side of the triangle and the extension of an adjacent side.
A remote interior angle is an interior angle that is not adjacent to the exterior angle.

19. Angle-Angle Similarity
Similar figures have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

20. Pythagorean Theorem

21. Distance Formula

22. Volume of Cylinder, Cones, and Spheres

23. Surface Area

24. Cont. Surface Area

25. Solving Linear Equations & Inequalities
We want to put all the variable terms on one side of the equal sign/inequality symbol.
Also we want all of the constant terms on the other side.
To move a term to the other side, you must do the inverse (opposite) operation.

26. Transformations

27. Cont. Transformations Remember:
270 degrees clockwise is the same as 90 degrees counterclockwise
270 degrees counterclockwise is the same as 90 clockwise

28. Dilations
Dilations change the size (but not the shape) of a figure.
Every dilation has a fixed point called the center of dilation.
Located where the lines connecting corresponding parts of figures intersect.
Also it gives you the scale factor.
The scale factor is the ratio of a length of the image to the corresponding length on the original figure.
A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction).
The scale factor describes how much the figure is enlarged or reduced.

29. Scatterplots
A scatter plot is a graph with points plotted to show the relationship between two sets of data.
A cluster is a set of closely grouped data.
An outlier is a data point that is very different from the rest of the data in the set.

30. Trend Lines
A trend line is a straight line that comes closest to the points on a scatter plot.

31. Mean Absolute Deviation (MAD)
A measure of center is a single number used to describe a data set.
One measure of center is the mean
the sum of the data values divided by the number of values in the data set.
A measure of variability is a single number used to describe the spread of a data set.
One measure of variability is the mean absolute deviation (MAD)
the mean distance between each data value and the mean of the data set.

32. Sampling
When information is being gathered about a group, the entire group of objects, individuals, or events is called the population.
A sample is part of the population chosen to represent the entire group.
A sample in which every person, object, or event has an equal chance of being selected is called a random sample.
A random sample is more likely to be representative of the entire population than other sampling methods.

33. Financial Literacy
Interest is the money that you pay to borrow money or use credit.
The interest rate determines in part the cost of a loan or of purchases on a credit card.
Simple interest is earned using the formula:
I = Prt,
where I is the amount of interest,
P is the principal, or the original amount deposited,
r is the interest rate expressed as a decimal,
t is the time in years.

34. Cont. Financial Literacy
Compound interest is interest paid not only on the principal but also on any interest that has already been earned.
The formula for compound interest is A = P (1 + r) ^t ,
where P is the principal,
r is the interest rate expressed as a decimal,
t is the time in years,
A is the amount in the account after t years if no withdrawals were made.