Mathnasium Training Exam Solved 100% Correct
10 rules of engagement - 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
A fraction - ANSWER-part of a whole.
A multiplication fact - ANSWER-has 2 factors and 1 product
A whole number - ANSWER-number without a fractional part—no common or decimal
fraction.
Addition With Half - 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).
Area - ANSWER-amount of space in a 2-dimensional figure, measured in square units
arithmetic - ANSWER-"the process of transforming one number into another, using
given rules."
Arithmetic - ANSWER-is "the Art of Counting." ari- (to join) + the + metic (measure)
Assign a Task - ANSWER-Concise but as long as necessary, Assign a task as you
disengage, 5-10 PK/Workout/HW exercises, Reassure that they can ask for help
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."
Checking out - ANSWER-Check workout plan goals and see if they've been
accomplished, Make a note on issues if necessary
Checkup - ANSWER-Comes before starting MFF program, Tests prerequisite skills
Correcting student work - 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
, Counting - ANSWER-transforms one number into another
Determine teaching method - ANSWER-socratic (ask questions), direct teaching, or
combination or both
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.
Direct variation - ANSWER-occurs for changing quantities x and y when y x = k, for a
constant value k
Distance - ANSWER-shortest amount of space between two points, and is measured in
linear unit
Dividing by half - ANSWER-"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?"
Division Tips - 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?'."
Documenting session progress - ANSWER-Mathnasium work, Footer #s of PK, Tally
pages, Homework spot check, Learning reflection
Every whole number and every fraction can be written three ways: - ANSWER-• as a
common fraction, • as a decimal fraction, • as a percent
Factor - ANSWER-a number quantity that when multiplied by and number equals a
product
Focus Ons (FOs) - ANSWER-extra practice, not grade related, general topics, adds
depth, advanced students, code at bottom right of each page
Fractions - ANSWER-created by dividing (cutting, breaking, "fracturing") a whole thing
into equal parts.
10 rules of engagement - 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
A fraction - ANSWER-part of a whole.
A multiplication fact - ANSWER-has 2 factors and 1 product
A whole number - ANSWER-number without a fractional part—no common or decimal
fraction.
Addition With Half - 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).
Area - ANSWER-amount of space in a 2-dimensional figure, measured in square units
arithmetic - ANSWER-"the process of transforming one number into another, using
given rules."
Arithmetic - ANSWER-is "the Art of Counting." ari- (to join) + the + metic (measure)
Assign a Task - ANSWER-Concise but as long as necessary, Assign a task as you
disengage, 5-10 PK/Workout/HW exercises, Reassure that they can ask for help
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."
Checking out - ANSWER-Check workout plan goals and see if they've been
accomplished, Make a note on issues if necessary
Checkup - ANSWER-Comes before starting MFF program, Tests prerequisite skills
Correcting student work - 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
, Counting - ANSWER-transforms one number into another
Determine teaching method - ANSWER-socratic (ask questions), direct teaching, or
combination or both
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.
Direct variation - ANSWER-occurs for changing quantities x and y when y x = k, for a
constant value k
Distance - ANSWER-shortest amount of space between two points, and is measured in
linear unit
Dividing by half - ANSWER-"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?"
Division Tips - 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?'."
Documenting session progress - ANSWER-Mathnasium work, Footer #s of PK, Tally
pages, Homework spot check, Learning reflection
Every whole number and every fraction can be written three ways: - ANSWER-• as a
common fraction, • as a decimal fraction, • as a percent
Factor - ANSWER-a number quantity that when multiplied by and number equals a
product
Focus Ons (FOs) - ANSWER-extra practice, not grade related, general topics, adds
depth, advanced students, code at bottom right of each page
Fractions - ANSWER-created by dividing (cutting, breaking, "fracturing") a whole thing
into equal parts.
