7th Grade CRCT Review ~ Major Concepts
Absolute value- means from zero on a number line.
Add/Subt/Mult/Div mix numbers, whole numbers
Always positive UNLESS there is a negative sign
and fractions (positives and negatives)
OUTSIDE of the absolute value symbol.
 Estimate sign of answer before you start!!!
 Convert any mix numbers to improper fractions
| 3| = 3
-|3| = -3
 When adding/subtracting –
|
-3|
=
3
-|-3|
= -3
MUST HAVE DENOMINATOR
 Method 1-Find Least common
Find the value of | -5 -8| =
denominator
1st solve inside the bars first, then find the absolute
 Method 2- just multiply the two
value of the number.
denominators to get a common
denominator
Ex. | -5 -8| = | -5 - 8| = |-13| = 13
 When multiplying/dividing (no common denominator)
Adding and Subtracting Integers (use a number line to
(remember convert to improper fractions, estimate
help you)
sign of answer)
- Use 1 as a benchmark to estimate answer size when
multiplying or dividing

If multiply by number greater than 1 the answer is
larger than what you started.
2 9 8 72
12
4
 4  4
Ex: - 3 15  2   
3 5 3 15
15
5
 If multiply by number less than 1 the answer is
smaller than what you started with.
2 9 2 18
Ex: 3 15    
7 5 7 35
 We cannot divide fractions, we multiply by the
reciprocal.
2  9 8 9 3 27

Ex: - 3 15    2      
3  5 3 5 8 40

(Note: Multiplying by number less than 1 gives a smaller
value, and same signs give positive answer)
Turn ANY subtraction problem to addition when
dealing with integers. Change the subtraction
symbol to plus, and change the number after the
symbol to its opposite.
Ex. -3 – 5 = (do keep-change-change)
-3 + (-5) = -8
Or
Use the circle method(circle the way you read)
+
-3 – 5 = -3 – 5 = -8
Negative 3 subtract 5 = negative 3 + negative 5
Integers Song (ONLY works for ADDING integers
so do Keep-Change-Change FIRST)

Adding integers song to the tune of row row
row your boat:

Same sign add and keep different signs
subtract, Take the sign of the greater value
then you’ll be exact.

Counters and Integers

Zero Pairs =
cancel out to zero
+3 + (-6) = -3
(3 zero pairs then see what is left? 3 negatives)

Horizontal and vertical number line
Ordering Rational Number - Know how to order
rational numbers from least to greatest or greatest to
least.(if numbers in different format, change to same
type (fractions to decimal, decimals to fractions)
 Integers only -Ex. Order from least to greatest
-3,-1, 2, 8, 0, -10
Answer: -10, -3, -1, 0, 2, 8
 Fractions/Decimals Combination
Ex: Order from greatest to least
2 10 3
 , , ,3.5
30 3 40
 Reduce fractions if you can first:
 Negatives are the smallest
Add and Subtract Decimals.
MUST line up the decimals.
Ex.
62 – 26.52 = 62.00
-26.52
Or
Use balance decimals methods
62.8 – 26.52 =
62.8 + 0.48 = 62.56
26.52+0.48 = -27.00
35.56
“of” that means to multiply.
Ex. 15 of 50 oranges is = 15 x 50 = 10.
Ex. 52 % of 80 is = 0.52 x 80 =
“Per” means to divide
“is” means equal
“And” means addition Ex. A product of a number and
two more than the number means - x(x + 2) parentheses
represents multiplication.
Measure of Central Tendency
Mean: average, add up all #’s divide by the amount of
numbers in list.
Median : order least to greatest, it’s the middle #
Mode: order least to greatest, it’s the # that appears most
often
Ranges: order least to greatest; subtract smallest # from
largest #.
MAD- Mean absolute deviation
Step 1-Find the mean of the data set.
Step 2- Find the distance each data value is from the
mean
Step 3- Find the mean of the distances
Large mad- tells us the data values have high
variability.(numbers are far apart, most times
includes outlier)
Small mad –tells us the data values have low
variability(numbers are close, most times no outlier)
Multiplying/Dividing – Integers Rules, fractions or
decimals
 Same signs positive, different signs negative.
Use 1 as a benchmark to estimate answer size
 If 3.5 ÷ 2 = 1.75
Dividing by number greater than 1
gives an answer smaller than you
started with.
 If 3.5 ÷ 0.8 = 4.375
Dividing by number less than 1 gives
you a larger value than you started
with
Multiply & Divide Decimals.
12.2 38.65
We cannot divide by a decimal. So, you must
change the divisor and dividend by shifting the
decimal over 1 space for this example.(you shift
to make the divisor a whole number)
122 386.5
Cross Sections of figures- Be able to determine the
cross section made by cutting a figure by a plane.
Determine what cross section results if the following figures
are cut parallel(horizontal) or perpendicular(vertical) to the
base.
Rectangular
Prism
Triangular
Prism
Cube
Rectangular/S
quare Pyramid
Triangular
Pyramid
Horizontal
Rect/square
Vertical
rectangle
Triangle
rectangle
square
Square/Rect
square
Triangle
Triangle
triangle
Data Analysis – Know how to analyze data in a
frequency chart, stem and leaf plot, circle graph, and box
and whisker plot.
How to read stem and leaf plots?
(2nd quartile)
( 1st quartile)

( 3rd quartile)

All congruent figures are always similar
however similar figures are not always
congruent.
Similar: ~ same shape different size

Congruent:  Same shape same size

Scale factor = model/original
 When scale factor question is written
Ex: Find scale factor of small to large:
Sf = small/large
or
Ex: Find scale factor of large to small:
Sf = large/smaller
Function and Equations- Understand what
happens to x and y values of the equation. Substitute
your own numbers to see. Always use low numbers
0, 1, 2 to determine decrease or increases. To verify
if set of coordinates fit the equation, make sure to
check all values.



y = mx +b or y = kx
Constant rate of change = slope = k = m
Slope= rise/run on graph
Area Ratios: the ratio of the areas of two similar figures
is the square of their scale factors Area(sf) = (SF)2
Perimeter Ratios: the ratio of the perimeters of two
similar figures is the scale factor. Perimeter(sf) = SF
Convert from fraction to decimal to percent and vice
versa.
Fraction to Decimal: divide numerator by denominator
Decimal to Percent: move decimal 2 places to the
right.
Percent to Decimal: move decimal 2 places to the left
Decimal to fraction: SAY the decimal properly and
you can write the fraction.
Analyze Function tables to determine equation x
0
1
2
y
1
2
3
What must I do to x to get y I can add 1 to the
value of X to get Y, Answer: y = x + 1
Hint: since x values show constant change, and y values
show constant change you can find the slope or the k of the
direct variation(directly proportional) by the output
change
+1
x
y
0
0
+1
1
-3
-3
-3
2
-6
y = -3x
Understand how to analyze the relationship
between x and y on a graph of a line.
As x increases, y decreases
Or as x increases, y increases
y
Direct Variation y = kx or x = k (to determine if
Inverse Variation - y =
an equation is direct, it must be in the form
where y is on one side of equal sign and k and
x on the other)
graph of inverse variation
 x increases , y increase (positive slope)
or
x increases y decrease (negative slope)
Direct variation line always passes through
(0,0) on a coordinate grid.
Solve Equations
Isolate variable by moving
everything to other side or substitute
answer choices into the problem and
choose answer that makes equation
true on both sides.
Solving inequalities
Isolate the variable the same way
you would an equation.
Remember, if you multiply or
divide by a negative number you
must change the direction of the
symbol.
k
x
or xy = k , k is
 x increases, y decreases or x decreases y
increase
Simply expressions. (Combine all like terms) to find
your answer.
Adding/subtracting expressions
 Find the difference between
(8w – 4g + 1) and (5w + 3g – 5)
( 8w – 4g + 1 ) – (5w + 3g - 5 )
Change all numbers in second expression to
opposite, then rewrite expression w/o parentheses

Distributive Property = 3( x + 4 ) = 3x + 12

Associative Property = (3a + 2) + (– 4a + 6)
8w + -4g + 1 – 5w - 3g + 5 = 3w + -7g + 6
= (3a – 4a) + (2 + 6) = -a + 8

Commutative Property = 7a – 8 + 12a – 9
= 7a + 12a – 8 - 9

Factoring expressions = 12a – 20b – 14
2( 6a – 10b – 7)

Equivalent expressions all of the above
problems represent equivalent expressions,
because the left side of the equal sign equals
the right side.
TRIANGLES AND ANGLE RELATIONSHIPS
 Triangle Inequality Theorem - x + y > z
x+z>y y+z>x
The sum of two sides of a triangle must be greater than the third side.

Triangle Sum theorem- The sum of all angles in a triangle must add up to 180
Probability
Likely hood of events occurring:
Independent vs Dependent
Independent events - probability that one event occurs does not affects the probability of the other event.
Example: Roll a number cube/ flipping a coin
Dependent events- probability that one event occurs does affect the probability of the other event
Pulling a marble out of bag, without replacement, then pulling a second marble out of the same bag.
Experimental vs Theoretical
Experimental =
Theoretical =
Data Analysis
Sample: part of the population (random, convenience
or biased)
Circle Graph - good for comparing parts to whole
Line Graph & Bar Graphs– good for showing
changes and patterns in the changes.
Simple random- pulling names out of a bag
Systematic random- every other 5th person
Bias- shows biased does not represent the population
due to bias
Population: the entire group
Census: a collection of data from an entire population
****************************Test Tips*******************************
READ THE QUESTION, READ IT AGAIN, SOLVE THE PROBLEM,
READ IT AGAIN!!!!
1) Use Process of elimination
2) Substitute answers choices for solving equations,
3) Check answers make sure they make sense,
4) Make sure you answer the question asked. Sometimes questions require
several steps to solve and test designers KNOW that you will forget some steps.
Therefore, they will offer several answer choices that you might get along the
way to solving the problem…just to make sure you are paying attention!