Mathnasium Training Exam
with Complete Solutions
100% Verified
When things are in proportion - 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: - Answer- • as a
common fraction, • as a decimal fraction, • as a percent
Rate - Answer- something happens for each or in each ("per") occurrence of something
else
Direct Relationship - 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 - 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 - Answer- Direct and Inverse
Direct variation - Answer- occurs for changing quantities x and y when y x = k, for a
constant value k
Zero - Answer- first number in our counting system
Negative numbers - Answer- numbers that are less than 0
Distance - Answer- shortest amount of space between two points, and is measured in
linear unit
Area - Answer- amount of space in a 2-dimensional figure, measured in square units
, Volume - Answer- amount of space in a 3-dimensional figure, measured in cubic units.
Problem Solving Strategy - Answer- If the whole is unknown, then the task is to build it
up from its known parts, If the parts are equal, we multiply; If the parts are not equal, we
add., The whole is equal to the sum (total) of its parts.
Blueprint for Change - Answer- Teach number facts as "the process of counting in
groups." • addition is "counting-up the total." • subtraction is "counting 'how far apart' two
numbers are." • multiplication is "a fast way to count equal groups." • division is
"counting the number of this group that are inside of that group."
Teach place value as - Answer- "the art of 'seeing' 10s.
The meaning of the Law of SAMEness - Answer- "You can only add and subtract things
of the same denomination, things that have the same name."
The Laws of Equality (the Laws of Transformation) - Answer- • "Equals operated on by
equals remain equal.", • "Equals may anywhere be substituted for equals.", and •
"Things equal to the same thing are equal to each other."
Teach the important properties of numbers - Answer- (Identity property, distributive,
cumulative)
Teach the Laws of Wholes and Parts - 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 - Answer- "the process of transforming one number into another, using given
rules."
Tier 1 - 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 - Answer- means have a conversation with the students
Tier 2 - 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 - 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)
with Complete Solutions
100% Verified
When things are in proportion - 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: - Answer- • as a
common fraction, • as a decimal fraction, • as a percent
Rate - Answer- something happens for each or in each ("per") occurrence of something
else
Direct Relationship - 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 - 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 - Answer- Direct and Inverse
Direct variation - Answer- occurs for changing quantities x and y when y x = k, for a
constant value k
Zero - Answer- first number in our counting system
Negative numbers - Answer- numbers that are less than 0
Distance - Answer- shortest amount of space between two points, and is measured in
linear unit
Area - Answer- amount of space in a 2-dimensional figure, measured in square units
, Volume - Answer- amount of space in a 3-dimensional figure, measured in cubic units.
Problem Solving Strategy - Answer- If the whole is unknown, then the task is to build it
up from its known parts, If the parts are equal, we multiply; If the parts are not equal, we
add., The whole is equal to the sum (total) of its parts.
Blueprint for Change - Answer- Teach number facts as "the process of counting in
groups." • addition is "counting-up the total." • subtraction is "counting 'how far apart' two
numbers are." • multiplication is "a fast way to count equal groups." • division is
"counting the number of this group that are inside of that group."
Teach place value as - Answer- "the art of 'seeing' 10s.
The meaning of the Law of SAMEness - Answer- "You can only add and subtract things
of the same denomination, things that have the same name."
The Laws of Equality (the Laws of Transformation) - Answer- • "Equals operated on by
equals remain equal.", • "Equals may anywhere be substituted for equals.", and •
"Things equal to the same thing are equal to each other."
Teach the important properties of numbers - Answer- (Identity property, distributive,
cumulative)
Teach the Laws of Wholes and Parts - 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 - Answer- "the process of transforming one number into another, using given
rules."
Tier 1 - 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 - Answer- means have a conversation with the students
Tier 2 - 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 - 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)
