NES Elementary Subtest II 2 Math Only (NO GEOMETRY)
2;4;8;16;32. Find the next number in the number pattern
64. This is an example of a simple number pattern. You are multiplying each number by 2 to get the next number. Unfortunately, this is probably too easy to show up on the exam.
Find the range: 56, 79, 80, 80, 93, 16, 16, 17, 5
88. Find the lowest (5) number and the Highest number (93). 93-5=88
Relations
< > < or equal, > or equal, =
Circle Graph or Pie Chart
A data display that uses pieces of a circle to show parts of a whole. This type of graph is used to show a percentage of a whole and will very likely show up on the test in a "which type of graph would be most appropriate?" type of question.
Histogram
A graph of vertical bars representing the frequency distribution of a set of data.
stem and leaf plot
A method of graphing a collection of numbers by placing the "stem" digits (or initial digits) in one column and the "leaf" digits (or remaining digits) out to the right. This is too hard to show in text format so do yourself a favor and google this. Know it well. It is extremely confusing if you are not familiar with the concept. It is on the test!!!!!....maybe.
Composite number
A natural number that is not prime.
Probability
A number that describes how likely it is that an event will occur. This is on the exam and will test or ability to differentiate between when to use the "addition rule" (p= and when to use the P(a or b) and the
Variable
A symbol used to represent a quantity that can change. For example, if we substitute 6 for the variable x, the value of the expression is 3(6) + 7 = 25.
inductive reasoning
A type of logic in which generalizations are based on a large number of specific observations.
Estimation
A way of making sure your answer is reasonable, rounding is a commonly used strategy
rational number
Any number that can be expressed as a ratio of two integers. Any number that can be a fraction. Remember that 0 is a rational number because 0/X is equal to zero. Also all integers are also rational numbers because they could be written as a fraction.
Find the Slope of a line
Change in Y over the Change in X
Teaching Scientific Notation
Scientific Notation is taught in 5th grade using division instead of negative exponents!!!! You may need to know that 1.5 x 10^-2 is equivalent to (1.5) divided by (10^2). Which are equal to .015.
mean
The average of a set of numbers
Estimation Strategy: Front End
The front-end strategy looks at the left-most or highest place value digit. You can estimate the sum 87 + 61 by adding the highest place value digits, 8 and 6. Thus, approximate 87 + 61 by 80 + 60 to obtain 140. NOTE: This IS in the study guide. I doubt it will be on the test because Rounding strategies are more relevant to the Elem. teaching world.
Integers
The set of whole numbers and their opposites {. . .-2, -1, 0, 1, 2. . .}. You may need to remember that all non zero ________________ are also fraction (e.g. 1/1=1, 5/1=5).
least common multiple (LCM)
The smallest multiple (other than zero) that two or more numbers have in common. For example, the least common multiple of 6 and 8 is 24 because 24 is the smallest natural # that is divisible by 6 and 8.
Estimation: Rounding strategy
Using rounding strategy to estimate 87 + 61 will round 87 to 90 and 61 to 60 leaving you with 90 + 60 = 150 as an estimate for the sum.
geometric sequence
a sequence in which each term is found by multiplying the previous term by the same number. example: 1, 20, 400, 8000, 160,000, 3,200,000 (multiplying previous number by 20)
Distributive Property
a(b + c) = ab + ac. Think about why we FOIL.
Find the general formula for the following sequences and then find a10, a50 and a100: 2;5;8;11;14;...
a1=2, a2=a1+3, a3=a2+3, a4=a3+3 etc. This formula won't be efficient because you would need to have the answer to the previous number to use it. So you need to think of this problem in terms of "how many multiples of three are there, relative to the amount of numbers are in the pattern. So for a2 think (3x1) + 2 or A2=3(2-1)+2, A3= 3(3-1)+2, A4=3(4-1)+2, A5=3(5-1),....A10=3(10-1)+2, A10=29, A50=3(50-1)+2=149, A100=3(100-1)+2=299 THIS TYPE OF qUESTION IS ON THE TEST BUT CAN ALSO BE SOLVED USING GUESS AND CHECK BECAUSE OF THE MULTIPLE CHOICE!!!
frequency distribution
an arrangement of data that indicates how often a particular score or observation occurs
Arithmetic Sequences
can be found by adding the same number to the previous term. A simple type of pattern like 1,2,3 or 2,4,6,8. You may encounter a question that asks you what the 100th number in a pattern like this would be.
unifix cubes
colorful, interlocking cubes that help children learn number and math concepts. They are especially useful for patterning. Also, for grouping for multiplication and division. Google an image to familiarize yourself.
Whole numbers
positive numbers, including zero, without any decimal or fractional parts. Includes all natural numbers plus zero.
range
the difference between the highest and lowest scores in a distribution
greatest common factor (GCF)
the greatest of the common factors of two or more numbers. For example, the greatest common factor of 27 and 18 is 9, since it is the largest number that factors both 27 and 18.
mode
the most frequently occurring score(s) in a distribution
numerator
the top number in a fraction
Point slope form of a line
y - y1 = m (x - x1); where (x1, y1) is a point on the line. FYI this is covered heavily in the study guide.
slope-intercept form
y=mx+b, where m is the slope and b is the y-intercept of the line. FYI this is covered heavily in the study guide.
mean formula
"The sum of observations / n" where n is equal to the number of observations.
Powers of 1
10^1=10, 253^1=253 etc.
Proportionality
A proportion is an equality of two ratios. A ratio can be expressed as a fraction like a/b = c/d or as a ratio a:b as c:d.
discrete variable
Consists of separate, indivisible categories. No values can exist between two neighboring categories.
Constants
Constants are the fixed values. In the expression 5x + 9, the constants are 3 and 7.
Natural Numbers
Counting numbers. 1, 2, 3, etc. Does not include zero.
Divisible by 5
The last digit is 0 or 5
Operators
The symbols with which you can specify the type of calculation you want to perform in a formula. x + - /
Divisible by 10
Umm, I think you got this one!!!
pictograph
a graph that uses a symbol that stands for an object. Usually accompanied by a key that demonstrates the value of each symbol.
10;7;4;1 Find the next number
-2. Subtracting 3 each step of the sequence.
What is the next number in this pattern 1, -3, 9, -27, 81,
-243. This is a geometric sequence. 1x(-3), -3(-3), 9(-3), etc.
Solve for the next number in the pattern: 1, 1/4, 1/16, 1/64, ...
256. This is a square pattern. start with a square and divide it both ways in half. Now divide each inner square both ways in half. Do it again, and again.
Solving a Proportion. Try if 2 pounds of carrots cost 80 cents, how much do 5 pounds cost?
2:80 as 5:N solve for N by cross multiplying fractions. So, 2/80 = 5/N. 2 x N = 2N and 5 x 80 = 400. 2N=400. N=200 The 200 represents pennies so the answer is 2 pounds of carrots would cost $2.00.
Find the mode: 44,29,13,44,15
44. You WILL get a question this easy on the test. Don't blow it!!!
Finding a pattern
Identify any numerical, algebraic, or geometric repetition in the problem. Guess how to extend the pattern, and determine if that guess is correct. THESE ARE ON THE TEST AND THEY WON'T BE SIMPLE PATTERNS!!!! THINK EXPONENTS, FRACTIONS AND SQUARE ROOTS. PRACTICE THEM!!
divisible by 8
If the last 3 digits form a number that is divisible by 8, then the number itself is also divisible by 8. For example, 1135 is divisible by 8 since 135 is divisible by 8.
Divisible by 3.
If the sum of the digits is divisible by 3, the number is also. For example, 159 is divisible by 3 since the sum of its digits is 15 (1 + 5 + 9 = 15), and 15 is divisible by 3.
divisible by 9
If the sum of the digits is divisible by 9. For example 27 is divisible by 9 because 2 plus 7 equals 9 and nine is obviously divisible by nine.
Base Ten Blocks
These are plastic cubes, rods, flats, and blocks used to teach place value. Cubes represent ones, rods represent tens, flats represent hundreds, and blocks represent thousands.
Cuisenaire Rods
They are small wooden rods of different lengths and colours. They are used to teach basic operations, parts of whole, fractions, sorting and counting.
Attribute Logic Blocks
This type of block is used for classifying, sorting, and ordering. They can also be used to explore size, fractional relationships, and geometric shapes. Be sure to google an image of them.
Bar graphs
This type of graph is a chart with rectangular shaped bars that have lengths proportional to the values they represent.
Adding Fractions. Try 2/3 + 4/5.
To add fractions the denominators must be equal. So you can multiply 2/3 by 5/5 to get 10/15 and multiply 4/5 by 3/3 to get 12/15. Now 10/15 + 12/15 = 22/15 (adding the numerators straight across). 22/15 is an improper fraction and cannot be reduced so it will have to be written as 1 + 7/15 on the exam. Remember this same method can be used for subtracting fractions, just subtract the numerator instead obviously.
Solve: Jay goes to Karate at least one day per week, but never on two consecutive days. List all the numbers of days per week that Jay could go to Karate.
1, 2, 3, or 4. This problem was on the study guide and is tricky because if you are too smart you will get it wrong.... For the test you must isolate your answer to only consider one week. Do not assume a continuum. So Jay can do Karate on Sun, Tues, Thu, and Saturday. A smart person would say only 1, 2 or 3 considering the next week not being able to go on Sunday... DON'T DO THIS!!!
Find the mean of these numbers: 5, 8, 17, 20, 0
10 (5+8+17+20+0)/5=10
10 to the X Power
(10^0=1, 10^1=10,10^2=100) Notice the pattern. The exponent dictates the number of zeros to the right of the 1. A negative exponent dictates the number of zeros to the left of 1 (10^-1= 1/10 or 0.1, 10^-2=1/100 or 0.01)
1;4;9;16;25; Solve for the next number in the pattern
36. This is a simple squared number pattern. 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25.
histogram vs bar chart in simple terms
A bar chart measures different non numerical categories. Like frequency of hair styles chosen some tuesday at a hair salon. A histogram would measure a numerical value on both the x and y. Like how many haircuts where given each month for a year the the said salon. The bars on the histogram are always touching each other so that reading trends is easier.
histogram vs bar chart
A histogram represents the frequency distribution of continuous variables. Conversely, a bar graph is a diagrammatic comparison of discrete variables. Histogram presents numerical data whereas bar graph shows categorical data. The histogram is drawn in such a way that there is no gap between the bars.
scientific notation
A method of expressing a quantity as a number multiplied by 10 to the appropriate power. IMPORTANT!!! You will NEED to remember that only one integer can be to the left of the decimal for proper scientific notation. For example 1,113,000 written as 11.13 x 10^5 is solvable but is not proper notation. It would have to be written like this: 1.113 x 10^6.
Prime number
A natural number that has exactly two factors, 1 and itself. Examples (2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37 etc.)
negative exponent (shown by "-^")
A negative exponent indicates a reciprocal and is the result of repeated division. For example 2^-3 = 1/8. Shown by 1/2=1/2, (1/2)/2=1/4, (1/4)/2=1/8. Or 1 × 1/2 × 1/2 × 1/2 = 1/8. Remember 2^-3 is the same thing as 1/(2^3).
Powers of zero
All Powers of zero are equal to 1. Search "powers of zero explained" on Youtube for a great Khan Academy explanation.
Manipulatives
An object which is designed so that a learner can perceive some mathematical concept by manipulating it. The use of manipulatives provides a way for children to learn concepts in a developmentally appropriate, hands-on and an experiencing way. Mathematical manipulatives are used in the first step of teaching mathematical concepts, that of concrete representation.
Story Problem: A college student receives one score of 82, one score of 88, and two scores of 89 on tests in a history class. Is it possible for the student to receive an average score of 90 if each test is 100 points possible?
Average = (sum of each attempt)/(number of attempts). So for this problem you would have [(sum of each attempt)+X]/(number of attempts plus the attempt that has not been tried) = 90. So it would be (348+X) / (4+1=5). You can isolate the (348 + x) by multiplying both side by 5. Giving you 348+X=450. Now you can subtract the 348 from the 450 telling you that a score of 102 would be needed and therefore the student will need to beg the Prof. during his office hours for an A-.
Associative Property
Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication
Real numbers
Combining the rational numbers with the irrational numbers results in this set of numbers. Includes numbers with non-repeating and non-terminating decimals (think of pie as an example) as well as all rational numbers.
Problem Solving Strategies: Solve: Bradly, Bre, Cameron, and Jaksen are entered in a car race. Bre is having tire trouble and is the slowest. Cameron is faster than Bradly but slower than Jaksen. What is the finishing order of the cars? NOTE: This type of problem was on my test!!! Maybe not this easy...
Make an orderly list to order competitors. Jaksen, Cameron, Bradly, Bre.
Solve 2.3 x 10^-3
Move the decimal 3 places to the left. .0023.
Solve 2.3 x 10^3
Move the decimal 3 places to the right. 2,300.
IMPORTANT!!! READ THE BACK OF THIS CARD IF YOU ARE TAKING PEARSONS NES SUBTEST II FOR ELEMENTARY!!! ALSO, DO I WOULD NOT RECOMMEND TAKING THIS EXAM REMOTELY BECAUSE YOU ARE NOT ALLOWED TO USE SCRATCH PAPER IF TAKING REMOTELY!!! MANY OF MATH PROBLEMS ARE VERY DIFFICULT WITHOUT SCRATCH. THE OFFICIAL PRACTICE TEST IS MUCH SIMPLER TO DO WITHOUT SCRATCH THAN THE ACTUAL TEST!!! TRUST ME ON THIS...OR DON'T...
Pearson front loads the test with very tricky questions that take a lot of time. I Highly recommend skipping the first 30 questions at first and doing them last. Don't even look at them!!!! Most of the questions on the last 2/3rds of the test are quick and sometimes easy. (if you are prepared.) It took me 40 minutes to do the first 15 problems on the exam and I freaked out and was SURE I would run out of time well before I could finish. I said "forget it" to the math and skipped the rest of it. Sure enough the last 40 questions only took me 20-30 minutes so I had plenty of time to go back carefully complete everything I left behind. Another option would be to flag and skip every problem that looks like it will take more than a minute. I got a 281 but probably would have done a lot better if I didn't get so rattled at the beginning of the test. I took 2 years of calc in college a long time ago (science side not easy arts side calc) and still found the questions unfamiliar, VERY awkward, time consuming and tricky. GOOD LUCK!!!!
Deductive Reasoning
Reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.)
Divisible by 6.
The number is divisible by both 2 and 3. So run both the 2 and 3 divisibility tests and you are good to go!!!
Multiplying fractions. Try 1/2 x 2.
When multiplying fractions we multiply the numerator and the denominator straight across. So for 1/2 x 2 you need to look at 2 as a fraction. 1/2 x 2/1. Now multiply the numerators to get 2. Then, the denominators to get 2. Your answer is 2/2 which is equal to 1. For the test you will need to understand what a model for multiplying fractions looks like. Youtube "Khan multiplying fractions model"
Rounding
You may need to round numbers to the nearest place and also nearest decimal. For example 35 rounded to the nearest ten is 40. 3.356 rounded to the nearest 100th is 3.36. I pray that you already know how to do this (:
Dividing Fraction. Try (3/4) / (1/2).
You will need to understand not only HOW to divide fractions but WHY dividing fractions makes sense. Youtube "dividing fractions model" because the test will have either the fraction division or multiplication model on it. (3/4) / (1/2) is as simple as multiplying one fraction by the reciprocal of the other. So 3/4 * 2/1 = 6/4 reduced to 3/2 or 1 + 1/2.
Probability Rule of Addition Practice: A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?
1/6 + 1/6 - 0 = 2/6 reduced to 1/3. The reason we subtract 0 is because that is how the formula works. [P(A)+P(B)] - P(A and B). A die is mutually exclusive meaning that you cannot get more than one outcome per role. In probability there are many circumstance that this is not the case. Think about this problem if we had two dice instead of just one?
Convert a fraction into a decimal in your head. Try it with 3/8.
First do you know what 1/8 is? If not do this. Start with a familiar component of this fraction. Like 4/8 = .5. Now half of .5 is .25 (or 2/8), Now half of .25 is .125 (or 1/8). Each eight is worth .125 so now .125 + .125 + .125 = .375. So 3/8 converted to a decimal is .375.
denominator
The bottom number in a fraction
Percentage to a decimal and fraction. Try 5%.
5% is equal to .05 or 5/100. Pay attention for the pesky % sign on the exam. There is a significant difference between .5% and 5% and .5.
(5/8)x
5/8 of a number represented by x
6,9,14,21,30,41, Find the next number in the pattern
54. This is a two part number pattern. You are likely to get one problem with this level of difficulty on the exam. 1^2+5=6,2^2+5=9,3^2+5=14, etc. and so on....7^2+5=54.
Convert a decimal into a fraction. Try it with 3.208.
First, you need to remember that the decimal 3.208 is equivalent to the mixed number 3 + 208/1000. Now you must reduce the fractional part of this number to lowest terms. Both 208 and 1000 can both be divided by 8. Resulting 3.208 = 3 + 26/126, Further reduced to 3+13/63. Be confident that the exam will only ask you to reduce fractions that somewhat friendly.
Place Value made complicated
For the test you will need to understand basic principles of place value. For example the 8 in 34,899 has the value of 800. But you may also have a question that checks for your understanding of place value using more complicated structure. For example: The number 945 = [(9 × 10^2) + (4 × 10^1) + (5 × 10^0)]
Dividing Fractions Model
For the test you will need to understand what a model for dividing fractions looks like. Youtube "dividing fractions model"
Multiplying Fractions Model
For the test you will need to understand what a model for multiplying fractions looks like. Youtube "Khan multiplying fractions model"
Divisible by 7 Rule.
Note that this rule is not in the official study guide for the NES subtest so don't sweat it. But remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. For example, to test divisibility of 12264 by 7, we simply perform the following manipulations: 1226 - 8 = 1218 121 - 16 = 105 10 - 10 = 0 Thus, 12264 is divisible by 7. YIKES!!!
Communative Property
Number order can be changed without changing the answer. For example 1x2=2 and 2x1=2. Works with addition and multiplication.
irrational numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating. These numbers cannot be shown as a fraction.
Probability Rule of Addition Practice: In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student?
P(girl or A) = P(girl) + P(A) - P(girl and A). (13/30 + 9/30)- 5/30 = 22/30 - 5/30 = 17/30
Find the Median: 1, 2, 4, 10
The Median is three. (2+4)/2=3. When there are even numbers of observances you must take the average of the two numbers that fall in the middle.
Reduce Fractions. Try 45/105.
You will divide the top and bottom by the Largest Common Factor. Or at least try to. For me I see that it is obvious that both of these numbers can be divided by 5. So, 45/5=9 and 105/5 = 21. Now you can reduce 9/21 again because both of these numbers can be divided by 3. Which equals 3/7. So a quicker way to solve this problem would have been to divide both the numerator and the denominator by 15 but doing this in two steps is easier for me especially under test pressure.
median
the middle score in a distribution; half the scores are above it and half are below it. Depending on an odd or even number of observations it is calculated differently. REMEMBER!!! The median is NOT a calculation of the middle. You cannot just take the low and high and find the middle. The median must be either the central outcome that occured (odd number in set) or the average of the two central outcomes that occured (even number in set).
1;3;6;10;15;21. Find the next number in the pattern
28. This is a triangle number sequence. Think about bowling pins lined up in a triangle. The first row has 1. The second row has two. The third row has three and so on. I am more numbers oriented so I would solve this problem like this. 1+2=3, 3+3=6, 6+4=10, 10+5=15, 15+6=21, 21+7=28. This is the level of difficulty that you should expect on the exam if not harder. I got a exponential number pattern that was crazy. It took me forever to work out but I got it eventually.
0, 1, 1, 2, 3, 5, 8, 13, 21. Find the next number in the pattern.
34. Fibonacci sequence. This is a very popular number pattern. You are adding the two most recent numbers together to get the next number in the sequence. I would at least be familiar with it. I did not have this pattern on either the WESTB or NES.
Solve this common proportion problem: a 5 foot vertical pole casts a 3 foot shadow. A tree casts a 20 foot shadow. find the height of the tree to the nearest tenth.
5:3 as n:20. solve for n by cross multiplying. It is important that you set this problem up correctly. Both theterm-113 tree heights need to be on either the top or the bottom. Both the Shadow lengths need to be on the top or bottom. Then cross multiply. 5/3 = n/20. So 5x20=100 and 3xn = 3n. So 100/3= n=33.3.
Divisible by two.
Easy peasy lemon squeezy.... The number is even.
Story Problem: Natalie purchased a USB Drive for her computer for $16.00, a mouse for $4.75, a keyboard for $9.00, and an HDMI cord for $6.25. What fraction of the total price of the supplies was spent on the USB drive?
Fraction of total money spent on paper = (amount spent on USB / Total amount spent. Or 16/36. reduced to 4/9.
Exponentiation (shown by "^")
Repeated multiplication. An exponent is often called a power. For example, the third power of 2 is: 2^³ = 1 × 2 × 2 × 2 = 8
if-then statement. Solve: In a fraternity with 31 members, 18 take mathematics, 5 take both mathematics and art history, and 8 take neither mathematics nor art history. How many take art history but not mathematics?
The Answer is 5. To solve this problem it is helpful to build a VINN diagram. Two overlapping circles. 5 will be in the overlapping section. 18-5=13 will be in the math section. 8 will be out of the circles all together. Solve for the art history only section by figuring out how many students are left over. 31-18-8=5. Which is 5. Be careful not to subtract the "5 both students" twice. THIS IS ON THE TEST. I had it on the West B and also the NES. This question is unsound because it doesn't explicitly state that the unknown students took art history. In the real world they probably took neither so don't be thrown by the unrealistic nature of the question.
Divisible by 4
The last two digits are divisible by 4. For example 144. 44 is divisible by 4. 11x4=44. So 144 / 4 = 36.
Find the Median from this set: 1, 9, 10.
The median is 9. Remember that median does not really mean "middle" in terms the the range. It just means middle number/s in the set.
Multiplication rule of probability
The multiplication rule is a way to find the probability of two events happening at the same time. There are two multiplication rules. The general multiplication rule formula is: P(A ∩ B) = P(A) P(B|A) and the specific multiplication rule is P(A and B) = P(A) * P(B). P(B|A) means "the probability of A happening given that B has occurred". You tube this and it will become way easier to understand.
Reciprocal
The multiplicative inverse of a number. For example the multiplicative inverse 5 is equal to 1/5. Or 1/3 is equal to 3/1. Remember that a number multiplied by is multiplicative inverse is 1 (e.g. (1/2)*(2/1)=1)
Pattern blocks
These are useful manipulatives for teaching geometry and fractions. Students can manipulate triangles, squares, hexagons, trapezoids, and rhombuses to build compound shapes, explore symmetry and transformations, & to solve problems.
measures of central tendency
This provides descriptions of the middle values of a data set. Includes mean, median and mode.
Line Graph
This type of graph displays information as a sequence of data points connected by straight line segments. This type of graph is best used to identify trends or patterns over time.
3K
Three times a number represented by K
Divisibility Tests
To find the prime factorization of a number, it is helpful to know a few tests for divisibility. There is a high probability that you will have one or questions on the exam that will force you to use one of the more difficult divisibility tests.
Probability Addition Rule
What is the probability that either A or B will occur. Find the probability of A and add it to the probability of B then subtract the probability of getting both outcomes A & B with one attempt. P(A. [P(A)+P(B)] - P(A and B). No comprende? Youtube "probability addition rule"
When should concrete manipulative be used???
When first introducing a new mathematical concept. Also consider them for intervention obviously.