Math
no more than 3
includes 3...
Order of Operations(PEMDAS)
1. Parenthesis 2. Exponents 3. Multiplication or devision, moving left to right 4. Addition or subtraction, moving left to right
Stages of learning math
1. concrete representations use manipulatives to introduce a concept. 2.symbolic or representational stage. -students draw pictures or symbols to represent the math concept 3. abstract stage: where numbers & variables are used to represent the concept
1m
100cm
85 is 120% of what number?
120/100=85/x
the sum of the interior angles of a circle
360°
the volume of the sphere
4/3πr^3
Tom wants to mentally calculate a 20% tip on his bill of $40. Which of the following is best for Tom to use in the mental calculation of the tip?
40×.1×2
John's car can drive 50 miles per gallon of gas, he wants to take a trip that is 750 miles. Gas currently costs $3.45 per gallon. He drives an average of 60 miles per hour during the trip. Which of the following expressions can solve for how many gallons of gas must he purchase for the trip?
750÷50: the 750 miles traveled divided by the 50 miles per gallon his car can travel
Standard Deviation
An average of how far each data point is away from the mean. -a higher standard deviation indicates higher variability in the data(the data are more spread out0
Which culture is credited with developing the use of negative numbers?
Chinese
Which metric prefix indicates a factor of 10?
Deca-
A kindergarten class is beginning a unit on data collection. Which of the following would be the best first activity?
Give each student a collection of colored tiles to sort by color -After sorting, students can begin to answer questions like, "what color of tile do I have the most of?", & "And the least of?" They can even begin comparing what they have with what another student has
Mrs. Gore is teaching about simple and compound events in probability. As she walks around the room, she has students draw a marble from a bag and answer the probability of drawing certain colors. What is the main motivation for teaching it this way?
Giving students an interactive way to learn
In a 1st-grade class, the students have been working with manipulative materials & pictures as they investigate the concept of addition, Through both formative & summative assessments, the teacher has determined that the students are ready to more abstract(pencil & paper) ways to represent addition. How should she begin this process?
Have the children model pictorial representations of problem like 7+2=9that include the numbers that represent each step -students learn best by doing, not by watching others do
Mrs. Stallings wants her students to learn the divisibility rules before committing them to memory. Using Bloom's Taxonomy levels, how can she elevate her lesson from"Remembering"?
Have them explain how to use the rules for large numbers. :this allows them to analyze the rules which is a higher level of Bloom's Taxonomy.
Suppose Monica's actual weight is 122 lbs. Her scale says her weight is 99.82 lbs. What can be said about her scale?
It is precise.: the scale is precise because it is reporting her weight to hundredths of a pound.
finding a perimeter of a triangle
P= a+b+c
students in Mr. Miller's class are given a worksheet with the different combinations that can be reached when flipping a coin & rolling a standard die. Students then work in pairs to flip & roll all of the combinations. What topic is Mr. Miller teaching?
Sample space: the lest of all possible outcomes
the people of the Arabian Peninsula(アラビア半島)
adopted(選ぶ)& adapted(適応する)the system of numbers originated by Hindus. -the Hindu-Arabic number system is used today worldwide
A plane
an infinite "surface" with no thickness that extends infinitely in all directions -non-collinear points
A thematic unit
an organization of curriculum around a central theme. :thematic planning lends itself to the integration of music, science, social studies, reading, writing, & math into a cohesive, interdependent unit
fraction decomposition
breaks down a fraction. -the fraction will keep its denominator the same & the numerators will add up to the original fraction. ex. 5/8 can be decomposed in a variety of ways: 1/8+1/8+1/8+1/8+1/8 or2/8+3/8
in a geometric sequence "r" means
common ratio
line graphs
connect data points with line segments -are helpful when plotting changes in data over time ex. looking at trends in weather such as rainfall over time
Which of the following units is most appropriate to measure the volume of a solid?
cubic centimeters
in a geometric sequence "a1" means
first term
A teacher's goal in a math lesson to have students extract data from various charts & displays. What is the best way to do this?
give each student a chart or display & have them create questions & then trade with a partner. : creating questions & discussing answers with a partner demonstrates mastery of a concept at a high level of learning
constructivism
learning new behaviors by adjusting our current view of the world ex.is best used for brainstorming rather than test preparation as it requires students to use what they know to predict new things to learn -group work or research projects a teacher provides her students with cubes of various colors & instructs them to create a pattern of their own. after the students each created a pattern, they will take turns presenting & explaining their patterns. -having the students research, create a presentation, & then present that idea to the class
Weight
ounces(mg) ounces(g) pounds(kg) tons(metric tons)
Capacity/Volume
ounces(ml) cups(ml) pints(ml) quarts(l) gallons(l)
collinear
points that lie on the same line
finding an are of a circle
r^2π
credit union(信用金庫)
similar to banks, but often based on a locality or professional affiliation.
in a geometric sequence "n" means
term number
supplementary angles
two angles whose sum is 180 degrees
complementary angles
two angles whose sum is 90 degrees
what percentage of 58 is 12?
x/100=12/58
Ms. Hughes wants students to be familiar with quantities from everyday life. She asks all students to report their height & weight so the class can calculate their mean, mode, & range. What is this a bad idea?
-Students might not be comfortable disclosing that info. -Students might not know that info. -Students are not actively engaged if they measured quantities themselves. :students would be more engaged in a hands on activity.
dot plots
-a graph that uses dots to show the frequency counts of a group of data -are used for small sets of quantitative data
Addition
-add(ed) to -all together -both -combined -in all -increase by -more than -perimeter -plus -sum -total
multiplication
-area -multiplied by -of -per -product of -rate -times -triple -twice
Which of the following would be an appropriate time for a classroom teacher to use a formative asses
-as a closing activity at the end of a class period -when students are involved in a cooperative group project -as the teacher is introducing a new concept
Graphs used to display categorical(categories/groups)data:
-bar graph -line graph -pie chart
Which of the manipulative materials below would be most suitable for teaching decimal notation to the hundredths place?
-base ten blocks -decimal squares
inductive(誘導の) reasoning/generalizing knowledge from one area to another
-broad statements are made from some data. - -creates -conjectures(憶測) ex. Snikers is a candy bar& Snickers have peanuts, therefore all candy bars have peanuts. a boy notices that dogs have four legs and a tail. When he sees a cat he incorrectly calls it a dog.
Real numbers
-can be rational or irrational rational numbers: numbers that can be expressed as a ratio(fraction or comparison) integers(-4,-3,-2,-1,0,1,2,3,4),whole numbers(0,1,2,3,4), & natural numbers(1,2,3,4)
subtraction
-decreased by -difference -fewer than -how many more -left -less -less than -minus -remaining -take away
division
-divided -half -how many each -out of -percent -quarter -quotient of -percent
graphs used to display quantitative(numbers)data:
-dot plot -stem-&-leaf plot/stemplot -box-&whisker plot -histrogram
a relation is a function if
-each input gives only 1 output -okay if each input gives the same output
which of the following are statistical experiments?
-flipping a coin 12 times -rolling a die 6 times in a row -rolling two dice until you get doubles
informal measurement
-footsteps -arm lengths -book lengths -pitcherfuls -counting seconds -buckets
a rectangular pyramid
-has a one base -has 2 triangular faces
Adjust Gross Income(AGI)
-income after deductions -the income amount taxed by the government
Which of the following sentences is true?
-integers include all natural numbers(1,2,3,4), whole numbers(0,1,2,3,4), &their opposites(negative numbers) -all irrational numbers include a symbol such as square root or pi
Weight
-is affected by gravity & will changed based on gravitational force.
Mass
-is constant -the mass of an object relates to how much matter it contains -grams
≥
-is greater than or equal to -is at least -is no less than
≤
-is less than or equal to -is no more than -does not exceed -at most(最大限でも)
≠
-is not equal to -is not the same as
linear equations from words
-look for the word "initial" or "start" to clue you into the starting cost, which is usually the y-intercept -look for the word "per" to clue your into a rate, which is usually the slope ex.the recurring monthly fee -look for the word "maximum"(<+_)& "minimum"(>+_) to clue you into an inequality
Secondary school
-one is called middle school(grade 6,7,8) -the other is called high school (grade9-12)
A new 5th-grade teacher is planning her math lessons for the grading cycle. She thinks of all of the topic she needs to teach & makes discrete daily lessons. Each unit has an opening pre-test. Each lesson has instruction, guided practice, & independent practice, Which of the following are methods she should incorporate into her lesson planning?
-plan each lesson with a closure activity -instead of making single lesson plans, first create a thematic unit around which to frame her lessons -plan time each day for students to explain concepts they have learned to their peers
Matching the sign of the slope with the direction of the line
-positive slopes should increase from left to right(uphill) -negative slopes should decrease from left to right(downhill)
Using money in mathematical examples is a good strategy to promote student engagement in activities. A 1st-grade teacher decides to begin teaching about place value by using money, specifically with the example of 10pennies=1 dime and 10dimes= $1. Why is this strategy probably not a good beginning strategy?
-the coins are not proportional with respect to shape & size -most young leaners would rather have 8 pennies rather than 1 dime -the relationships above are too abstract for young learners
the perimeter of an object
-the distance around the outside of that figure -a one-dimensional measurement -inches(in.) -feet(ft.) -miles(mi.) -millimeters(mm) -centimeters(cm)
an equation & an inequality
-the solution to an equation is usually one number the solution to an inequality is usually a range of numbers
deductive reasoning
-true statements are used to make a proper conclusion -can be used to evaluate conjecture validity -Caitlin knows that all boys like cars. Adam is a boy. Therefore, Caitlin concludes that Adams likes cars. -using 2 or more known premises to draw a conclusion ex. 1.All cats say meow. 2. Jackie is a cat. 3. Therefore we can deduce(憶測する) that Jackie says meow.
bar graphs
-use bars to show comparisons between categories of data -helpful when displaying the amount of data within each category
When analyzing the table to see if it's linear(look for a constant rate of change)
-write the equation in slope-intercept form(y=mx+b). Identify the y-intercept by: 1. looking for (o,b) in the table 2. working backwards to (0,b) in the table 3. Plugging x & y values from the table into the equation & solving for b
Matthias wants to find 20% of 70, using mental math. Which of the following numbers is best for Matthias to use to multiply by 70 to find the correct answer?
0.2 :most students at this level will know 7×2=14, & they will be able to move the decimal mentally.
graphing y=-2/3x-4
1. identifying the slope(m) & the y-intercept(b) m= -2/3 b=-4 2.Plot the y-intercept(-4). Begin with b 3.count the rise & run of the slope-checking that the line is increasing or decreasing accordingly in this equation, the slope is -2/3, so the line should be decreasing(from left to right)with a rise of +2 & a run of -3 *Rise=numerator=vertical(x) *Run=denominator=horizontal(y)
A 6th-grade teacher is beginning a unit on probability. She utilizes the following steps in planing her unit
1.Plan the final assessment for the unit 2. Determine the necessary prerequisite skills 3, determine what the students already know by using a KWL chart 4.Begin planning probability activities that involve the collection of data
the volume of a cone
1/3πr^2h
Malik wants to find 25 percent of 84 by doing a mental calculation. Which of the following numbers is best for Malik to use to multiply by 84 to find 25 percent of 84?
1/4
the odds(可能性)of rolling a 4
1/5 :there is 1 way to have a successful outcome(rolling a 4)& 5 ways to have an unsuccessful outcome(1,2,3,5,6) :in order to find the odds, you need to add all the remaining objects together for the denominator odds: the likelihood of success to unsuccessful events
the probability of rolling a 4 on a standard six-sided number cube(die)
1/6 probability: the likelihood of success out of total events
of the following, which is most likely the distance from a classroom on the second floor to the playground outside at the end of the wing?
105meters :it is about the length of a football field -a meter is close to a yard which is the actual unit for measuring a football field
Julie brings & eats 1/2 of a sandwich every day for lunch. If she made 11 sandwiches this month, how many lunches did she bring? Which of the following expressions would be a correct computation for the answer to the problem above?
11÷1/2 :this expression would equal 11×2/1, which equals 22, the correct amount of lunches
If a number ends in zero, what number(s) can it be divided by?
2&5 not 4
if a number is divisible by 6&8, what other number(s)can also divide into it?
2,3,&4
Approximately what fraction of the population is within one standard deviation of the mean in a data set with a normal distribution?
2/3 68.2% of the population will be within one standard deviation of the mean.
1 year
52 weeks
Which of the following civilizations is most closely associated with the development of algebra?
Arabian
Which of these statements correctly describes the coefficients & degrees of the polynomial shown? 5x^7 + 5x^5 -3x -2
Coefficients:5,-3,-2 Degrees:7,5,1,0 constants are noted as 0 degrees(because x^0 =1)
Which of the following activities would best allow a teacher to demonstrate an appreciation for cultural diversity in a math class?
Discuss the average wage & cost of living for cities around the world -
Students in Miss Pappa's class each have a set of cards with numbers 0-9 on them. When they have a few minutes in class, she asks students to pull out the cards & they create large numbers with them. She will then ask students to hold up the card with a place value of 10, 100, 1000, etc. Why is this a good teaching practice?
Every student participates & this reinforces the concept regularly.
Adam wants to determine how much to charge for an event. He looks through his records from old events to determine a reasonable price for the venue(会場), the average price of catering, & thinks about other incidentals(雑費). He then solicits(懇願する)quotes from several people & places before setting a price for the event. What process is he using to create this budget?
Formal reasoning: is used to answer questions & solve problems that have a single solution(a right answer) by using rules of logic & algorithms(systematic methods that always produce a correct solution to a problem)to reach a conclusion.
Which of the following statements is false?
Inductive reasoning never leads to a correct conclusion -may or may not lead to a correct conclusion. it is incorrect to say that inductive reasoning never leads to a correct conclusion.
students are working on measurement principles. Kali measures a counter top in the classroom that is 5,743 mm long. Lauren finds that the distance on a map between New York City & Washington D.C. is drawn as 364.1mm How does the 3 in Kali's number compare to the 3 in Lauren's number?
Kali -5,743 Lauren-364.1 -1/100 Kali's digit is in the ones place & Lauren's digit is in the hundreds place. Therefore, Kali's digit is 1/100 of the value.
international system of units(SI)/the metric system
Kilo- (1000) km,kl,kg Hecto-(100) hm,hl,hg Deca-(10) dam,dal,dag Base units(1) m,l,g Deci-(0.1) dm,dl,dg Centi-(0.01) cm,cl,cg milli-(0.001) mm,ml,mg
Behaviorism
Learning new behaviors based on the response they get to current behaviors ex. if a students studies for a test(current behavior) makes a good grade(response)they will learn to study for tests(new behavior)
Ms. Todd gives students a project where she gives all students in her class a single set of ordered pairs numbered 1 through 30. They need to graph ordered pairs in order & then connect the dots in the order in which they are graphed to make a picture. This serves as their final unit project on graphing points on the coordinate plane. Is this a suitable project?
No, because students can easily copy each others work: since all students receive the same ordered pairs copying may be rampant(広まる)& students may not be demonstrating mastery
Ms. Kelly has been teaching fractions & believes her students understand composing & decomposing fractions through the activities they have done. What activity would be best to informally assess their knowledge before moving on to the next lesson?
Provide a warm-up question that asks them to write one way to decompose 3/4
Which of the following is the best way for elementary students to be introduced to rectangular arrays?
Using manipulatives such as 10-blocks to create their own arrays
finding a volume of a cone
V=1/3πr^2h
finding a volume of a sphere
V=4/3πr^3
finding a volume of a cylinder
V=Bh
the volume of a cylinder
V=Bh or V=πr2h
finding a volume of a rectangular prism
V=lwh=Bh
A 2nd-grade class has created a pictograph of what type of shoe each person is wearing. What is the next visual representation students can make from the info given?
a bar graph -cab easily be created from a pictograph & mimics the same shape. This is scaffolded for the children to learn how to create a bar graph
A prime factor
a factor that is also prime ex. 2&3 are prime factors of 6, because 2×3=6 & 2and3 are also prime
normal distribution
a graph with a bell-shaped curve -1σ+μ+1σ=68.2%(roughly 2/3 of the data is within one standard deviation of the mean) -2σ+μ+2σ=95.4% -3σ+μ-3σ=99.7%
improper fraction
a larger number in the numerator such as 7/2
a variable(4)
a letter or non-numeric symbol that represents an unknown value, ex. x, y, z, q
transversal(横断線)
a line that intersects 2 or more(often parallel)lines
A fair coin
a mythical(根拠のない)gadget(装置)which has a probability exactly 1/2 of showing heads & 1/2 of showing tails each time it is tossed.
a coefficient
a number that multiplies a variable 2x+4y-9z
margin of error (in stats)
a number that represents how far above or below the actual mean may be from the experimental mean in a study
A factor
a number which can be multiplied together to get another number. ex. 2 & 3 are factors of 6, because 2×3=6
a constant
a number without a variable. ex. +10,-10
a system
a set of 2 or more equations or inequalities with the same set of variables, or unknowns. ex. 2x+3y=13 & 4x-y=5 x=2 y=3
A funtion
a special type of relation where each input(x value) has only one output(y value) -A quick way to check for a function is to find any repeated values in the x column. -having the same x-coordinate causes the two points to align vertically on the graph -the graph of a function must pass the "vertical line test"
a line of best fit/trend line
a straight line that best represent the data on a scatter plot
the English system/the imperial system
a system of measurement used in the United States using units such as feet, pounds, & ounces
axiom(原理)/postulate(必要条件)
a truth that is accepted as being self-evident
histogram
a visual representation of data, similar to a bar graph, which compares frequencies of different occurrences
The school district provides a 50 multiple-choice question mathematics assessment to all students. the students complete the assessment, the tests are scored, & the scores are compared throughout the school district. Which of the following mathematics component is most likely the goal of this type of assessment?
accuracy: because it is multiple choice
fraction composition
add together fractions with like denominators ex. 1/4+1/4+1/4=3/4
Mr. Chappel hangs posters in each corner of the room with different names of number categories. One corner has a sign that says integers, another has a sign that says rational numbers, another says irrational numbers & the last says whole numbers. Students are assigned a corner to start & on the first rotation they must add a definition to the sign. On the second rotation, they must add numbers that are examples to the sigh. What should be the third rotation task?
adding a picture that helps students remember what is included in the number set. :this continues to familiarize students with the number sets
slope
change in y/change in x ex. the change in y is +3& the change in x is+2 the change in y is +3= 3/2 This pattern of adding 2 to x & 3 to y could continue forever
for a student with strong addition skills, which subtraction algorithm is most suited their skill set?
counting up: this method adds numbers to the smaller number to reach the larger number.
speed
distance/time
reducing fractions
dividing the numerator & denominator by any common factors to put the fraction in lowest terms ex. 80/96 to 5/6
more than 3
does not include 3 so 4 or more. to include 3, say "3 or more"
finding a circumference/perimeter/ surface area of a circle
dπ
a term
each part of an expression that is separated by a + or -sign. ex. 2x, 4y, -9z, -10, q
a quadratic relationship
ex. as side length(x) doubles , area(y) quadruples(4倍の)
variable costs
ex. electricity & gas bills, spending on consumable goods(groceries), discretionary(任意の)spending
curriculum-based assessment
ex. informal assessments(exit tickets), group discussions, homework assignments, anything that builds upon previous activities & helps assess a student's achievement in a particular area :comparing students' mastery of a standard or skill over a period of time to gain more complete understanding of a student's abilities over the course of the unit
criterion-referenced
ex. most normal tests or quizzes used by teachers : comparing students performance to specific criteria or standards
norm-referenced
ex.an IQ test :evaluating a student compared to his peers not used to "grade"the student
fixed costs
ex.car payments, mortgage(住宅ローンz) payments, & recurring dues
standard measurement
feet, inches, cups, gallons, meters, centimeters, grams, etc.
Mrs. Blue wants her students to be able to write two column geometric proofs. Which is the most appropriate way to determine their mastery?
give students an open ended exam where they write multiple 2 column proofs: asking students to write a proof is the best way to determine if they can write a proof
conjectures(憶測)
guesses without proof while doing mathematics
a rectangular prism
has two bases(rectangles)that are parallel to each other
A teacher has her students graph multiple linear equations with the same slope, & then record their observations about the equations & graphs. Which of the following goals is the teacher most likely to achieve?
have students connect the relationship between equations with the same slope & parallel lines: having students graph a series of equations with the same slope & record their observations will help students connect that all equations with the same slope but different y-intercepts will produce parallel lines
when identifying slope-intercept form..
identify 2 points along the line such as (0,8)&(-5,0). Then determine the slope(rise/run:y^1-y^2/x^2-x^1) This allows to identify the equation as y=-8/5x+8
Mr. Lee shares a scientific study on stimulus & response in rats with the class. As a class, they draw conclusions from the study. He then asks them to find potential flaws in the study. What goal is Mr. Lee trying to achieve?
identifying key components of a valid study: students who can identify the key components of a scientific study can identify potential flaws in the research & conclusions.
relative prime
if two numbers have no shared factors(besides 1), two numbers are relative prime. ex34 & 15 are relatively prime because 34=2×17 &15=3×5, & there are no factors in common the LCM can be found by 34 ×15 or 510
Another way of representing the slope
in a linear equation, the slope is rise(y)/run(x) slope intercept form:y=mx+b m-the slope b-the y-intercept
Units for length
inches(mm) inches(cm) feet(decimeters) yards(meters) miles(kilometers)
A mathematics teacher gives her class a two-question clicker quiz at the end of each class period and tabulates their answers according to their mathematical understanding, misconceptions, and error patterns. If her goal is improvement in her students' mathematical proficiency, her best use of the data would be to use it to:
inform upcoming instructional strategies -data on student understanding, misconceptions, & error patterns is best used to inform instructional strategies on the same or subsequent topics
Janine is trying to determine who to vote for in the class president race. She thinks that candidate A is friendlier to her, but candidate B is better at convincing adults to do things. What type of reasoning is she using when she decides who to vote for?
informal reasoning: is used to answer questions &solve problems that are complex & open-ended without a definitive solution by using everyday knowledge to synthesize info & reach a conclusion. Janine is using feelings rather than true logic in her decision making here.
the precise use of mathematical language
is required when using & describing info in the coordinate plane
Informal reasoning
is used to answer questions & solve problems that are complex & open-ended(without a definitive solution) ex. do you support the city implementing a bike-sharing program?
formal reasoning
is used to answer questions & solve problems that have a single solution(a right answer)by using rules of logic & algorithms ex. how much paint should we buy to paint the bathroom?
A relationship is described as linear if...
it has a constant rate of change & creates a straight line when graphed.
Suppose Mike's actual weight is 165 lbs. His scale says his weight is 164 lbs. What can be said about his scale?
it is accurate.
which of the following is true of a statistical experiment?
its outcome is determined by chance
cognitivism
learning new behaviors by connecting connect knowledge with new knowledge ex.if a student studies for a test by associating real world examples with the concepts such as learning fractions by slicing a cake into equal parts, they will retain the information.
A student asks that how much space a cube takes up. the teacher said to answer this question, the student would need to calculate the volume of the cube. Which of the following measurable attributes is the formula for a cube based upon?
length -before the volume of a cube can be calculated, the length, width & height must be measured.
backwards planning
lesson planning at all levels of instruction should begin with the desired outcome in mind -decide on the outcome first, then how mastery will be measured, then the lessons
skew(非対称の)
lines that are not coplanar & do not intersect
empirical(経験による)probability
looks at the exact percentage of outcomes that occurs in a real situation
Central tendency
mean, median, &mode
creating proportional ratios is only true with
multiplying/dividing If a number were to be added or subtracted from both the numerator and denominator, the result would not be a proportional relationship.
theorems(定理 )
must be proven before they can be accepted or used
Which of the following units represents the shortest distance?
nanometer: is equal to one-billionth of a meter
composite numbers
natural numbers that have numbers that divide into them ex. 4 is composite because it is equal to 2×2
the units
ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred million, billions, etc.
Mr. Yoder gave each of his students some Starbursts & some Skittles. He instructed the students to use the candy to set-up & solve multi-step equations, using the Starbursts to represent the x's, the Skittles to represent the constants, &different colors to represent positives & negatives. To solve the equations, students must determine how many Skittles are equivalent to one Starburst. Which of the following concepts is Mr. Yoder most likely working on with his students?
order of operations when solving equations: Suppose a student was solving 2x+3=5, & had 2 Starbursts & 3Skittle equal to 5 Skittles. Before they could figure out how many Skittles are equivalent to one Starburst, they must take away 3 Skittles so the Starbursts are by themselves before determining how to divide the remaining Skittles evenly among the Starbursts. Students will realize that is it not possible to determine how many Skittle represent one Starburst without first getting the Starbursts by themselves on one side. This allows students to discover that you must add or subtract the constants first before using multiplication or division to isolate the variable.
Maria has recently moved from Mexico City to the U.S. She is a secondary student who speaks little English, but who came from her school in Mexico City with excellent grades. Which of the following would be the most appropriate accommodation for Maria's math teacher to use with Maria?
pair Maria with another student who speaks Spanish, to clarify instructions in Spanish as needed.
which of the following is the most appropriate unit for expressing the volume of an average glass of milk?
pint: one pint is a volume of 2 cups & is best for expressing the volume of a glass of milk
Which of the following activities is most effective in helping kindergarten students understand measurement of the lengths of small items, such as juice boxes or lunch boxes?
placing same-size objects, such as Legos or cubes next to the object & counting the number of objects
coplanar
points with the same plane
Financial literacy
possessing the skills & knowledge on financial matters to confidently take effective action that best fulfills an individual's personal, family, & global community goals
Mr. Thomas is teaching measures of central tendency to his class that is mostly comprised of English Language Learners(ELL). What is the best support for teaching the new vocabulary words?
put the words on a Word Wall with the word, picture, & definition :Word Walls give students something to reference when thinking of vocabulary
the ancient Greeks
responsible for much of what is studied in Geometry(the Pythagorean Theorem)
Formal measures
rulers tape measures meter sticks protractors yardsticks measuring spoons & cups scales balances stopwatches
A student-athlete can run 10 yards in 6seconds. Which equation shows the number of yards that can be run in s seconds?
s/0.6 :if 10 yards can be run in 6 seconds, 1 yard can be run in 0.6 seconds. Therefore, the total number of seconds divided by 0.6 will give the number of yards run.
arithmetic sequence
sequences that have a common difference -the difference can be a positive or a negative
geometric sequence
sequences that have a common ratio, or multiplier(× or ÷to get to the next term) -the common ratio in the sequence is the amount you multiply by to get from one term to the next ex. 5,10,20,40,80
A 6th teacher discovers that each student in his class receives an allowance from their parents. Which of the following examples would best demonstrate to the students the power of saving their allowance instead of spending all of their allowance?
show students the expected return of 5% allowance savings over a 10-year period
The school district wants all elementary students to be able to use computational(計算)strategies fluently & estimate appropriately. Which of the following learning objects best reflects this goal?
students evaluate the reasonableness of their answers: if a student is able to use computational strategies, strategies for computing an answer, as well as estimate properly, then the student should be able to evaluate the reasonable ness of his final answer.
symbolic
symbolic representations use symbols or variables for students to work with. -are often encountered in math as formulas, ex. area=length×width
Property taxes
tax on the land & building people own. -are often used to fund schools & local services
How should a teacher instruct students to deal with remainders?
tell tem to multiply the decimal part of the solution by the denominator to see if it matches the remainder
the area
the amount of surface inside of a figure -a 2-dimensional measurement(length×width, for example) -square inches(in.^2) -square miles(mi. ^2) -square centimeters(cm^2) -square kilometer(km^2)
example of the y-axis(vertical)
the amount of the loan(dependable variable)
A student asks the teacher who invented the number system. Which of the following answers would be most appropriate?
the base-ten number system was developed by the Hindu-Arabic civilizations -the base-ten number system, which is the foundation of the modern number system, was developed by Arabic & Hindu civilizations
when a car is traveling 30 mph
the car travels 60 miles in 2 hours
range
the difference between the highest data & the lowest data value
a greatest common factor(GCF)/the greatest common divisor(GCD)
the largest factor shared by two(or more) numbers. in order to find the greatest common factor find the prime factorization of the numbers in question & circle all factors that are shared.
The student is expected to determine the value of a collection of coins & bills. Which of the following is an example of a clear learning goal for the TEKS skill stated above?
the learner will understand & explain the total amount of money they have when given money manipulatives
arc length
the measure of a section of the circumference of a circle ex. the length of crust on a slice of pie
vertical angles
the pair of opposite angles created when 2 lines(or line segments) intersect
prime factorization
the process of writing a number as a product of prime numbers or a product of prime factors and -1.
Using a proportion to solve for a missing value will work only if...
the relationship is proportional: the graph is a straight line that goes through the origin
magnitude
the size of numbers. (less than(<),greater than(>),equal to(=)
a least common multiple(LCM)
the smallest number two values will both divide into evenly -the lowest number that will equally divide by 2 integers
examples of the x-axis(horizontal)
the time in months(independent variable)
Ancient Sumerians & Babylonians
used base 60 number system(sexagesimal) approximately 5,000 years ago.
Which of the following is a developmentally appropriate activity for an average sixth grader to establish number sense?
using positive & negative numbers to represent financial situations
experimental probability
what actually occurs during a simulation or trial ex. when a real coin is flipped 10 times& the results are recorded. -rarely will a person actually get exactly 5 heads&5 tails from 10 coin flips
theoretical probability
what we expect to happen in theory. ex. if a coin is flipped 10 times, theoretically, one would expect to get 5 heads & 5tails
common denominators
when 2 fractions have the same denominator -in order to find it, first look for the least common multiple
Babylonians
where our modern system of time originates from. 60 minutes per hour & 60 seconds per minute -are also responsible for the convention of 360° in a circle
Payday lender(貸す人)
will give people short term loans at very high interest rates. -not a smart financial decision
point-slope form
y - y1 = m(x - x1)
f(x)
y-coordinate
the formula of finding the slope
y1-y2/x1-x2
an example of a linear equation
y=3 :since this equation only contains a constant, it is linear. y=3+0x
Which of the following equations is written in slope-intercept form?
y=3x+5: y=mx+b
the volume of a cylinder
πr^2h
