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MATHNASIUM TRAINING EXAM RETAKE
ASSESSMENT NEWEST VERSION 2025 WITH
COMPLETE QUESTIONS AND SOLUTION 100%
VERIFIED ANSWERS A+ GRADED
Individual instruction in a group environment - CORRECT ANSWER >>> many classes of
one
Team teaching - CORRECT ANSWER >>> instructors rotate on the floor, helping students in
strategic moments, students benefit from multiple instructors, Each instructor helps students individually
10 rules of engagement - CORRECT ANSWER >>> Use mathnasium teaching constructs,
try a new explanation if it isn't working, fall back on old knowledge when a student is struggling and expand knowledge with student is succeeding, praise and criticize constructively when appropriate, socratic vs direct teaching, use mathnasium vocabulary, use tools for visual learning, use metacognition, use mental math, master team teaching
Half and half model - CORRECT ANSWER >>> half HW, half mathnasium activity
Mathnasium model - CORRECT ANSWER >>> warmup, warm down, mathnasium
activities, HW
Guidelines for instruction delivery - CORRECT ANSWER >>> Sit across from students,
Supporting and encouraging voice, Be concise
GENE Teaching - CORRECT ANSWER >>> help a student for a while, allow them to be
independent, help someone else, then come back
The Student Binder - CORRECT ANSWER >>> Contains material from student learning
plan, assembled from assessment results
Sections 1-5 of binder - CORRECT ANSWER >>> Assessments and progress info,
Prescriptives in works (grade specific), A+ splits active packs and new packs, Workout books in works (development dependent, simple and helps with mathematical thinking), Corrected prescriptives, Corrected workout books
PKs (prescriptives) - CORRECT ANSWER >>> designed like typical math practice pages with
increasing difficulty ranging in length (2-22 pgs) (Don't tell them the PK level)
Instructional pages - CORRECT ANSWER >>> help instructors refresh on techniques
Mastery check - CORRECT ANSWER >>> mini-assessment, should be done independently
Focus Ons (FOs) - CORRECT ANSWER >>> extra practice, not grade related, general topics,
adds depth, advanced students, code at bottom right of each page
How to rotate and read the floor - CORRECT ANSWER >>> Look around see if students
have lost focus/talking/staring into space/asking for help/stuck on one page for a long time, Use peripheral vision to see if students are raising their hands while engaged with a student
How to appropriately engage students - CORRECT ANSWER >>> See how they're doing, Be
inviting and non threatening, Students will be self conscious to ease them in, See what they know to adjust your vocabulary, Scaffolding by working on easier stuff to work on what they have an issue with
How to disengage and communicate - CORRECT ANSWER >>> Once they have it figured
out, let them try it on their own and help someone else, Always leave them with a task
Checking out - CORRECT ANSWER >>> Check workout plan goals and see if they've been
accomplished, Make a note on issues if necessary
Instruction Teams - CORRECT ANSWER >>> Separate areas or student needs, Higher level
students may be sat separately from lower level, Ratio should not exceed 4:1 students to instructor
Team leader - CORRECT ANSWER >>> Center director or experienced instructor, Direct
students to seats, Check students in, Direct instructors, Delegate, Acknowledge students in need, Assist struggling students
Session Wheel - CORRECT ANSWER >>> Use to see student's productivity and
communicate for max productivity
Workout plan - CORRECT ANSWER >>> For director use, not for parents
Types of students interactions - CORRECT ANSWER >>> Normal instruction, Responsive or
proactive
Determine teaching method - CORRECT ANSWER >>> socratic (ask questions), direct
teaching, or combination or both
General approach - CORRECT ANSWER >>> demonstrate exercise; observe, comment
correct, ask Qs; disengage
Correcting student work - CORRECT ANSWER >>> Correct right away in front of stu, Stu
should not proceed until you review their page, Strengthen stu's understanding, Ask stu to explain their answer - correct or incorrect, Circle the exercise # of errors, Give page back for stu to correct, Box circled exercises to indicate a correction was made, Star punch when completely correct
Mastery checks - CORRECT ANSWER >>> Demonstrates mastery and independence, can
only be reviewed once completed independently, Review and return for stu to correct, Date and initial, Notes to center director if unable to complete MC
Student types - CORRECT ANSWER >>> Unruly, easily distracted or unwilling students,
Overloaded fatigued students, Quiet or shy students
Arithmetic - CORRECT ANSWER >>> is "the Art of Counting." ari- (to join) + the + metic
(measure)
Wholes and Parts, and the relationship between them - CORRECT ANSWER >>> unite
various aspects of math.
Proportion - CORRECT ANSWER >>> means "according to amount." pro- (according to) +
portion (amount)
Quantity - CORRECT ANSWER >>> is the amount of that something; the number of things
We can only add and subtract things that... - CORRECT ANSWER >>> have the same name,
things that are of the same denomination.
Number facts - CORRECT ANSWER >>> addition, sub, mult, div resulting in single digit and
some double digit number answers, These are things students must know in order to learn more advanced math
When they learn to count by ones ask - CORRECT ANSWER >>> "What number is 1
bigger/smaller than five? 2 bigger/smaller than 9?", THEN they should be asked "name 2 #s that add up to 5" or "what and 3 add up to five?", THEN "5 and how much more make 7?" and "8 is how much more than 5?"
The Power of 10 - CORRECT ANSWER >>> 10 is the base #, Stu must learn special
properties of 10, "The given # and how much more make 10?", Point out that teen = digit + 10, THEN move on to doubles (1+1, 2+2, 3+3...), THEN 1X is how much more than 10?, THEN 1X is how much more than 10, 9, 8, 7..., Avoid the use of terms like "commutative property" and "associative property" until well after the student has mastered the number facts.
Tips for teaching addition - CORRECT ANSWER >>> Start at x and count up to y, Doubles
+1, Doubles - 1, Breaking down #s (6 + = 8), How far apart are x and y?, How far is it from x up to y?, Combinations that make 10, 10 plus a number, 10 plus what number, Putting it all together
Subtraction tips - CORRECT ANSWER >>> Counting how far apart and how much is left:
The process of removing a part from a whole., Sub asks how much is left and how far apart are 2 #s, Use "how much is left?" when the numbers are fairly far apart, and count down. (~10), Use "how far apart are the two numbers?" when the numbers are fairly close to each other, and count up (<<10)
Multiplication Tips - CORRECT ANSWER >>> Instead of asking, "What is 5 times 4?" which
calls for a memorized response, a much better question form is: "How much is 5, four times?"
Division Tips - CORRECT ANSWER >>> Division is repeated subtraction, and answers the
question, "How many of these are there in that?", How many groups of 3 are there in 12? How many times can 3 be taken out of 12? How many times can 3 be subtracted from 12 before the answer is less than 3?, The written process of division should not be started until the student can reliably, orally answer questions like these: How many 10s are there in 30? How many stacks of 5 can you make out of 20 pennies? How many quarters are there in $3.00? ...in $4.50? How many 20s are there in 100? How many 125s are there in 1,000? How many 15s are there in 60?, Say "'15 divided by 5' means 'How many 5s are there in 15?'."
- CORRECT ANSWER >>> The numerator "the one that numbers." It tells us how many of the parts to use this time When the numerator is less than the denominator, as in 3 4, the value of the fraction is less than
1. Why? Because if you have 3 out of 4 parts, you don't have all of it yet. You are 1 part short. -
CORRECT ANSWER >>>
When finding half of an uneven fraction - CORRECT ANSWER >>> breaking a number into
easier parts, • finding half of those parts, and • then putting the parts back together again
Addition With Half - CORRECT ANSWER >>> "One half plus one half equals a whole" is the
basic notion required for adding fractions., Then, "two and one half plus three and one half" can be thought of as: "two plus three is five" (add the whole numbers), "one half plus one half equals a whole" (add the fractions), and "five and one are six" (combine the results).
Subtraction with half - CORRECT ANSWER >>> WRONG: "Seven take away two and one
half" is often answered by students as "five and one half" because they subtract the whole numbers and just "bring down" the half, RIGHT: Hold up seven fingers, five on the left hand and two on the right, and say, "Here are seven." • Next, put down the two fingers on the right hand and say, "I've taken away two, so how many are left?" (Five.) • Then say, "I have five left. Now I'll take away the half, so how much is left?" Now, fold down the first joint of the thumb of the left hand. (Four and one half.)
Multiplying BY half - CORRECT ANSWER >>> "three and one half, two times" means
- CORRECT ANSWER >>> "three, two times, and one half, two times." Saying "3½, two times" does this; saying "2 times 3 ½" doesn't. Dividing by half "Three divided by one half" can be thought of as "How many halves are there in three wholes?" or "How many half sandwiches can you make out of three whole sandwiches?"
ORDER - CORRECT ANSWER >>> more than half - less than half
A whole number - CORRECT ANSWER >>> number without a fractional part—no common
or decimal fraction.
A fraction - CORRECT ANSWER >>> part of a whole.
Unity - CORRECT ANSWER >>> A fraction whose value is equal to one whole
Proper fraction A fraction whose absolute value is greater than or equal to zero (0) and is less than one whole
Improper fraction - CORRECT ANSWER >>> A fraction whose absolute value is greater
than one whole (1).
Place Value - CORRECT ANSWER >>> Whole numbers are formed by counting by 1s,
decimal point, a marker that separates the whole numbers (on the left) from the fractions (on the right)
PER CENT - CORRECT ANSWER >>> Percent is an appropriate topic for first and second
grade students if it is presented as an outgrowth of Counting, Wholes and Parts, and Proportional Thinking., Reverse questions involving percent take the form, "10% of what number is 40?"
Ratio - CORRECT ANSWER >>> "a comparison between two numbers by division"
When things are in proportion - CORRECT ANSWER >>> the relationship between the
parts stays the same even though one or more of the parts changes in value; as the amount of one thing changes, both the relationship between the object and the whole, and the relationship between the object and the other parts, stay the same
Every whole number and every fraction can be written three ways: - CORRECT ANSWER
>>> • as a common fraction, • as a decimal fraction, • as a percent
Rate - CORRECT ANSWER >>> something happens for each or in each ("per") occurrence
of something else
Direct Relationship - CORRECT ANSWER >>> As one quantity gets larger, the other
quantity gets larger by the same amount. As one quantity gets smaller, the other quantity gets smaller by the same amount.
Indirect (Inverse) Relationship - CORRECT ANSWER >>> As one quantity gets larger, the
other quantity gets smaller by the same amount. As one quantity gets smaller, the other quantity gets larger by the same amount.
Variation - CORRECT ANSWER >>> Direct and Inverse
Direct variation - CORRECT ANSWER >>> occurs for changing quantities x and y when y x =
k, for a constant value k
Zero - CORRECT ANSWER >>> first number in our counting system
Negative numbers - CORRECT ANSWER >>> numbers that are less than 0
Distance - CORRECT ANSWER >>> shortest amount of space between two points, and is
measured in linear unit
Area - CORRECT ANSWER >>> amount of space in a 2-dimensional figure, measured in
square units
Teach the Laws of Wholes and Parts - CORRECT ANSWER >>> • "The whole is equal to the
sum of its parts." • "Any one part is equal to the whole minus all of the other parts."
arithmetic - CORRECT ANSWER >>> "the process of transforming one number into
another, using given rules."
Tier 1 - CORRECT ANSWER >>> Adding on to the larger # (adding 1 or 2 onto a larger #),
10 plus a single digit # (emphasizes that the 1 in the 10s place means 10, includes 10 and X more is 1X), decomposing single digit numbers (Do these numbers feel close together or far apart? The count FORWARD or BACK)
Let's talk about it icon - CORRECT ANSWER >>> means have a conversation with the
students
Tier 2 - CORRECT ANSWER >>> Addition facts Sums up to 10 (adding onto the larger
number without finger counting), Complements of 10 (uses language from tier 1, puzzle piece helps visualize complements of 10), Doubles facts, subtraction facts Minuends up to 10 (builds upon up to and take away ideas to introduce subtraction, and find how much is left)
Tier 3 - CORRECT ANSWER >>> Addition facts over 10 (uses doubles, up to or over ten,
and add/take away 10 and what method works for you), Subtraction Facts/MIssing Addends, Minuends Over 10 (scaffolding for up to and over 10 technique)
Numerical Fluency - CORRECT ANSWER >>> Automaticity, learn by heart, effortless recall
The Problem with Memorization - CORRECT ANSWER >>> When they forget the answer,
they have no way of getting around it because they lack understanding and strategies, Without strategies, stu uses inefficient techniques or wild guess
Factor - CORRECT ANSWER >>> a number quantity that when multiplied by and number
equals a product
A multiplication fact - CORRECT ANSWER >>> has 2 factors and 1 product
Multiplicand - CORRECT ANSWER >>> aka factor, but the first one multiplicand x factor =
product
Multiplication fact - CORRECT ANSWER >>> a complete mult equation with 2 factors and a
product
Multiplier - CORRECT ANSWER >>> aka factor but the second number
Repeated Addition - CORRECT ANSWER >>> adding multiple times
Turnaround facts - CORRECT ANSWER >>> commutative property; n * m = m * n
Methodology - CORRECT ANSWER >>> builds on foundation of add/sub using prerequisite
knowledge, efficient techniques, structured practice, engaging activities
Multiplication War - CORRECT ANSWER >>> Each player turns over 2 cards, and the player
with the highest product wins that round
Multiplication Heads Up - CORRECT ANSWER >>> each player can see the value of the
card on their opponent's forehead, but not the card on their own forehead, after the moderator tells the product, players race to state the value on their heads
Multiplication with Dice - CORRECT ANSWER >>> Declare a #, stu rolls dice and finds
product of your number and their number OR roll 2 dice and stu finds their product
Go Fish Tac Toe - CORRECT ANSWER >>> Stu claims spaces on TTT board by finding pairs
of cards that are factors of each product
Multipliganos - CORRECT ANSWER >>> stu identifies as many mult facts as they can from
a grid of dominoes
