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CT Math

Terms in this set (141)

The teacher could best help the students understand that the triangle is equivalent to half a square by showing them how to:
Create a reflection of the triangle along its longest side
The greatest benefit of providing elementary students with mathematical tools such as geoboards is that these tools —
Provide students with visual representation that promote their conceptual understanding
The fifth grade math teachers at Smith Elementary have assigned the students a coordinate grid project to assess student understanding and mastery of the concept. In assessing the project, what should the teachers provide in order to evaluate the projects?
A rubric so that project expectations are clear from the beginning
The teacher uses the smart board in his classroom to access a website with a large hill. The teacher used _________ to assist students in developing, comprehending and applying mathematical concepts.
Technological tools
Shortly after, Ms. Jones was dismayed to see that the students were not making much progress. Some were already off-task and many others were complaining that the task was too difficult.What can be said about Ms. Jones' action in the scenario of this question?
Her discourse cut off opportunities for discovery by giving the students the information they needed rather than asking probing questions to get them to the solution of the task
First grade students learning math fluency have been using several methods to support their learning. Which of the following would be the least effective method for first graders to learn math fluency?
write the fluency vocabulary
A first-year math teacher visiting Mrs. Wilson's classroom quickly observes the tasks have "real world" context, require an explanation, involve multiple-steps, and are "text-like" but, require no manipulatives and show no connection to meaning. Which of the following best describe the reason Mrs. Wilson most likely chose the tasks for her students?
To increase students speed and accuracy
Miss Anderson then models solving a long division problem with the algorithm. Which algorithm could Miss Anderson be using to teach long division?
First divide, then multiply, then subtract, bring down the next digit and repeat these steps
How much will the sweater cost Samantha if she applies both the 25% off sale price and her 20% employee discount?
$60
An early childhood teacher will be introducing the concept of skip counting by 2s. In order to implement the lesson as a hands-on, concrete and visually stimulating activity, which of the following would best demonstrate the concept for the students?
Using a hundreds chart from 1-20 and having the students cover every other number with a sticky note
Which number system is a repeating decimal a member of?
rational
Express 0.7083 as a fraction.
17/24
Fifth graders are learning about linear functions and how to best model a set of data. What kind of graph could best be used to model a set of data representing years and average income in those years?
scatterplot
Three times the width of a rectangle plus five is the same as seven more than four times the width. If W is used to represent the width of the rectangle, which of the following expresses this relationship?
3w + 5 = 4w + 7
Students learning to solve for missing values through input/output tables which increase the output (or y value) by the same value are laying a foundation to be able to work with which kind of function as they mature in their mathematical knowledge?
linear functions
A first grade teacher is planning a lesson to engage algebraic reasoning for the students. The teacher will first model two sides of an equation using base ten blocks then write the equation for the students to see the relationship between the model and the expression. What other model would be beneficial for students in making connections between the concrete and the abstract in algebraic reasoning?
Pictorial Model
A first grade teacher is teaching algebraic reasoning through problems which present to the students as if they are puzzles. One way the teacher could do this is to introduce students to a card game in which they must find the missing addend. What could be the teacher's goal with this method?
The teacher's goal is to use the concept of learning through play in order to strengthen the students' number sense and introduce algebraic reasoning.
The teacher has asked the students to find the area of this regular polygon. What steps might the students take in order to solve the problem?
Partition the figure into two rectangles by drawing a horizontal imaginary line then solving for the area of each rectangle and adding them together.
Students in first grade are practicing counting money by the amount in a collection. Students are then writing the value of a collection of coins. Which common mistake may NOT occur in the course of students learning to write the value of a collection of United States coins and bills?
$5.67
In order to develop, justify and use conversions within a measurement system, the teacher will arrange the classroom in collaborative grouping so students are able to practice measuring mass then converting it within the system. Which measurement system will the students be working with in this collaborative setting?
Metric system
The students in fourth grade are solving for the missing angles in triangles. The students have been given the following graphic and instructions to solve for the missing angle. What equation would best solve for the missing angle?
60 + 60 ____ = 180
Fifth graders learning about coordinate planes and graphing ordered pairs,Which of the following would NOT be a characteristic the students would have explored when being introduced to coordinate planes?
There are four quadrants in a coordinate plane, and quadrant 2 and quadrant 3 are positive.
The students in a kindergarten class will collect data about the number of children in each classmate's family. What might be the goal of this activity?
The goal is for students to take ownership of their learning and investigate to gather info.
Ms. Chen will facilitate the collection of the data and guide students to make a bar-type graph. For what could this bar-type graph be useful?
Drawing conclusions and generating and answering questions about the data
The students in Mrs. Young's fourth grade class were asked to investigate the amount of milk the cafeteria needed to order for one week based on data collected on current orders, student preferences and predictions for future use. What standard are the students exploring through their investigation?
Probability and statistics to investigate real-world problems
Each student has been given a small package of colored chocolate candies. The students will sort and classify their candies by color and the number of candies of each color. Students will then make a chart and a graph to show the number of each color in their packages. This activity supports which of the following TEKs?
collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts
Which of the following would not be considered an acceptable form of mathematical representation?
written sentence
Which of these would NOT be an effect of technology on math curriculum?
Technology will make math less important
Third grade students are exploring the area of rectangles. To provide a hands-on investigation, the teacher has provided rectangle templates in various shapes and sizes and square crackers. To further the investigation and justify their solutions, what next step must students take?
Prove their solutions by comparing them with other classmates and with the findings of the teacher
The teacher instructs the students to use their knowledge of place value to describe a number in more than one form. Which of the following indicates different forms of a number a student could use?
Standard form, Word form, Expanded form, Expanded Notation
There are times when an exact amount is needed and times when an estimation is acceptable. What are two acceptable forms of rounding numbers which teachers are required to teach as dictated in the TEKS?
Estimating numbers and finding compatible numbers
Based on the descriptions above, these activities will promote development of map skills to second graders mainly because they —
help students learn abstract map concepts through involvement in concrete experiences related to a familiar location.
Which of the following questions would best promote students' ability to apply the concept of relative location?
Is the book shelf or the piano closer to the aquarium?
Why are these skills vital to a students' overall academic and citizenship development?
As students develop historical thinking skills they can use the same analysis skills as adults to evaluate political, economic, and social arguments and perspectives and be well-informed citizens.
Mrs. Granato would like to introduce her students to careers and professions which use math in the workplace. Which of the following TEKS might Mrs. Granato be able to apply to this lesson? Select all that apply?
Develop a system for keeping and using financial records
Balance a simple budget
Identify the advantages and disadvantages of different methods of payment
Describe actions that might be taken to balance a budget when expenses exceed income
A teacher is introducing the concept of elapsed time to a third grade class. Which of the following could be the manipulative aids the teacher chooses to use?
T-Chart, number line, Judy clock
Mr. Taylor wants to introduce his students to the concept of place value. Which of the following sets of manipulatives best describe those that can effectively be used to teach this concept?
base-ten materials, decimal squares, 10-frames, cuisenaire rods,math balance, cubes, 2 color counters
Which algebraic expression would show the relationship between the input and the output?
Number x 10 = Value
Mrs. Green is introducing subtraction to her kindergarten students. Which of the following will be important for Mrs. Green to link to the concrete representation of the blocks as she checks for understanding with the students?
Pictorial Models and Blocks
The teacher is introducing comparing whole numbers in terms of greater than and less than. What mathematical comparative language should the students use to compare prices?
The oranges at store A are less expensive than the oranges at store B.
In order to relate rounding numbers to a real life situation, the teacher is taking the class on a virtual field trip of a grocery store. Which mathematical processes would be applicable in this activity?
Rounding to the whole number, addition of whole numbers subtraction of whole numbers
The 3rd graders in Mr. Roberts class were asked to solve the following problems: Which method below would solve this word problem?
Add 10 plus 10 to find the total amount of money bobby has. Then multiply seven lollipops by 2. Finally subtract 14 from 20 to find the amount bobby has left after his purchase.
If the price of selling a pair of shoes is represented by the expression (300-x) where x is the number of shoes sold, the REVENUE FUNCTION is R(x) = _______?
x(300-x)
Amber's dog, Marc, eats $85 of dog food in 2 weeks. How much will Amber spend on dog food in a year?
$2210
Mr. Chen has asked his students to solve for the number of square feet of carpet needed to cover his living room floor with carpet. How should the students solve for the area of the room?
Students should multiply the length by the width to find the number of square feet.
Arrange from smallest to largest.
15 cm, 1 foot, 14 inches, 0.4 yard
Which of the following would define a line?
A line is a set of points that form a straight pathway extending infinitely in opposite directions.
The students in Mr. Young's fourth grade class were asked to investigate the amount of milk the cafeteria needed to order on data collected. What standard are the students exploring through their investigations ?
probability and statistics to investigate real world problems
The teacher is gathering on the students for the past three assessments given in het class. In looking for patterns and relationships within the data, for which variables will the teacher be looking?
Patterns in assessment grades over time and within similar concepts
Each student had been given a small package of colored chocolate candies. This activity supports which of the following TEKS ?
Collect, sort, and organize data in up to three categories using models/representation such as tally marks or t-charts
ABC ISD is improving it's curriculums through technology and hands on experiences. which of the following will provide a hands-on experience being able to manipulate rotate or transfer, and decompose three dimensional shapes?
visual media
As our need for mathematical literate workers and citizen increases our economic security will depend on how well we have educated other individuals and incorporated them full participation in the economy of the 21st century.
The need for trained workers will continue to rise in mathematically based careers in 21st century
Activity 1 and 2 Chart: based on the description above these activities will promote development of map skills to second grade math because they
help students learn abstract map concepts through involvement in concrete experiences related to a familiar location
Activity 1 and 2 Chart: which of the following questions would best promote students ability to apply the concepts of relative location?
Is the book shelf or the piano closer to the aquarium?
Which of the following types of investment is the safest but normally has the the lowest rate of return?
Savings account
Art
Music
Science
Social Sciences
Business
Tessellations
Patterns and Symbols
Mass
Changes in population
Budgets
Which response from Joe may have appeared on the Math Talks poster as a way to explain his thinking ?
I multiplied five times nine by counting by fives nine times
In a third grade class, 75% of the students failed the assessment over probability and data collection. What next step should the teacher take to re-teach and reinforce the assessed concepts ?
Reintroduce the concept to the whole class; then work with small groups of students to reteach the assessed concepts.
The perimeter of a rectangle is 380 inches. What would be the best approach for the teacher to respond to the answers ?
B. congratulate the students on their efforts of critical thinking through a tough question and their ability to calculate the area correctly.
Bowl question
> greater than
the connection between math and science
Which could be used to find two consecutive even numbers whose sum is 80?
no solution
First graders are applying skip counting as they count to 100. What are some things the teacher could be used to teach skip counting by 2s ?
socks, shoes, feet
given the task Of computing two consecutive even numbers whose sum is 50. determine the choice below that should represent the second number?
x + 2
Which of the following is divisible by six?
12960
what is the proper mathematical term for the symbol in this equation? 13 + _________= 18
variable
Input/Output Chart: Which expression might the students have written ?
x + 6 = y
Nissa and Alex are picking apples in the orchard. which expression Will help nissa and alex determine how many apples are in the first bucket?
? + 32 = 53
Three times the width of a rectangle plus 5 is the same as seven more than four times the width. which of the following expresses this relationship ?
3w + 5 = 4w + 7
which figure is two dimensional ?
triangle
which of the following identifies the geometric parts that good not be formed decomposing the rectangles?
two congruent rectangle, 1 circle
which of the following statements about the rectangle must always be true
The perimeter is even number
evaluate the reasonableness of converting 215 F to 101. 7 C
since the boiling point in Fahrenheit is 212 and the boiling point in Celsius is 100, The answer seems reasonable
The students in a kindergarten class will collect data about the number of children and each classmates family. what might be the girl of this activity?
The goal is for the students to take ownership of their own learning and investigate to gather information
what approach should the teacher take with the students who opted To skip the prediction step?
stop to observe, the students and correct the behavior
what information would the students need to collect in order to be able to show normal distribution Mrs. brown is requesting?
The number of students indicating their association with each culture
what might a student reason in order to apply deductive reasoning to complete the pattern
I can see the pattern increases So I must need add or multiply
Determine the choice that does NOT relate to the following:

10x + 5
solve for the value of x
what are two acceptable forms of rounding numbers which teacher are required to teach as dictated in the teks
estimating numbers and compatible numbers
Mr. Jansen's second grade students have been working on addition and are now ready to begin learning two digit subtraction......This approach best demonstrates Mr. Jansen's understanding that
Instruction in math should build on existing knowledge of math
Mr. Jansen's second grade students have been working on addition and are now ready to begin learning two digit subtraction......When considering the use of calculators for math exercises, Mr. Jansen should keep in mind that
Once students have demonstrated that they know the correct way to perform math calculations, they should be allowed to use a calculator
What might be the goal for Ms.Case having her students role play shopping and working in a store?
The teacher is planning instruction to demonstrate how math is used in a store in a scenario her students may experience on occasion
Mrs. Jones is preparing her fourth grade students for their field trips to the farmers market. Which instructional strategy could Mrs. Jones be implementing her students to maximize their time and efforts at the farmers market?
Real-World situations with budgeting and building meaningful coonnections
How does using a variety of assessment tools aid Mrs. Frankie in knowing her students understanding of the concept?
It allows Mrs. Frankie to evaluate mathematical understanding and discover misconceptions and error patterns
Mrs. Howard a first grade teacher, knows the importance of using assessment wisley and conscientiously in her classroom...... How is the formative assessment a better source of information than if Mrs.Howard gave a summative assessment every day after a math lesson?
The formative assessment can be delivered quickly.......
Which basic operations has commutativity?
Addition
256/4
To determine the divisibility rule they should apply to this problem
If the last two digits is divisible by 4
Which of the following is not prime number?
1
What is the multiplicative inverse of 0.5?
2
Second graders........How might the teacher represent this with the shaded regions?
Provide students with three rectangles: one cut in halves, one in fourths and one in eighths. Then have the students shade the parts and compare the size of each part to a whole.
Find the slope of the line....... (0,8), (-2,0)
4
Is the graph of a circle function? Describe why or why not ?
No. It does not pass the vertical line test
Which of the following does not represent an explicit rule?
3+6=9
Third graders...... What explanation may the students have given to know the areas are equal?
Students may be have decomposed rectangle A vertically and rectangle B horizontally; wheras reactangle A would have 6 rows of 2 to represent 1/2 and rectangle B would have 3 rows of 4 to represent 1/2.
Which attributes would be helpful for Mr. Brown to introduce to his class before the proceeding with the activity?
Ability to roll, number of corners, number of sides, number of flat surfaces
Formula: P =2(___)+2(____)= ______
P= 2(12)+2(5)=34
Which of the following is a semi abstract strategy for how the students would show the amount?
Students can explain and decompose the numbers, draw pictures of the money and write out how many one dollar bills, five dollar bills, and types and amounts of coins are needed
Find the mean of rainfall for 2011 by using the chart below.
4.87
In looking for patterns and relationships within the data, for which variables will the teacher be looking?
Patterns in assessment grades over time and within similar concepts
In what context is it important that students be exposed early on to diversity in acquisition of mathematical concepts?
All students need to be exposed so that more women and minorities will purse mathematical careers and broaden the field of experts across cultures.
What should the next step of the algorithm be?
Total amount invested - Principal
-0.25 + ___ = 0.15
The teacher is trying to get students to understand the concept of
Adding a positive and negative
How do these instructional activities show the teacher is planning age appropriate activities for her students?
The teacher knows that students this age learn to apply knowledge through song and physical activity
4 3/8 as a decimal
4.375
Mr. Jacobs fifth graders will work in small group to solve addition and subtraction of fractions......... When solving addition and subtraction of fractions with unlike denominators what will be important for students to remember and apply?
Students will need to make equivalent fractions using LCD prior to solving problems with unlike denominators
Which of the following, when applied to fifth grade concepts, would relate back to number bonds ?
Diagrams
In a fifth grade math class...... What prior knowledge of the students could the teacher draw on to relate percentages to real life situations?
The teacher should implement an activity relating fractions and decimals to percentages
Convert 45 F to _______ C
7.2 C
Which of the following units would teacher have available for students to measure capacity?
Gallon,quart,pint,cup,ounce
A quilt is made using the following pattern. This is an example of
2 dimensional geometric model
First grade student are exploring probability........Why is modeling the data collection and experiment important for the development and comprehension of the concept of probability?
The teacher knows to model and demonstrate a concept in terms that students can see and feel....
What is the probability that both a couple's last two children will be girls
1/4
Given the pattern shown above continues in the last two layers, use inductive reasoning to predict the pattern in the bottom layer of the triangle.
1+6+15+20+15+6+1
Third grade students are exploring rectangles....... To further the investigation and justify their solutions, what next step must students take?
Prove their solutions by comparing them with other classmates and with the findings of the teacher
What type of assessment techniques is the teacher utilizing?
formative
Which question would be appropriate for the teacher to ask if the math problem to be solved was 650 x 45
Explain how to solve for the product of 650 x 45
A store is having an end of the year computer sale. What is the total cost of a discounted computer system
$1,550.60
Which algorithm could Miss Anderson be using to teach long division
First divide, then, multiply, then subtract, bring down the next digit and repeat these steps.
Learning to skip count forward in lower grades in preparation for which of the following mathematical operations?
Multiplication
Which of the following is the correct expression to equal 24?
60/3 + 6 -2 x(-1)0
Which factor would indicate the importance of teaching rounding and estimation within mathematical computation?
To makes sense of problems and persevere in solving them
a/b=4, b/c=2, what is the value of a/b+c?
8/3
For which representation of the triangles is Mr.Brown asking his students to solve?
Numeric
What should Ms. Ramirez's role be during the time the students work in stations?
A facilitator at one of the stations to work with small group to also check in on the other stations
How could Johnny and his classmates check for reasonableness?
They can conclude that Elyse must be younger than her mom, so they could subtract 32-26= Elyse's age or 6 and then check by plugging in elyse's age to see if 32-6=26
What might a student reason in order to apply deductive reasoning to complete the pattern?
I can see the pattern increases, so i must need to add or multiply =. If I add........
Which of the following is not a reason as to why it is important that students be given the freedom to solve mathematical problems in more than one way?
The teacher has the correct way to solve each....
The teacher knows students prior knowledge of which concepts must be engaged in order for the lesson to be successful
Patterns, skip counting,reasoning making predictions
Which set of questions could the teacher use to have the students think at a higher level on the bloom's taxonomy chart?
How might we solve for this problem? Can explain what would this equation true?
Which common tools would be best for the teacher to use to demonstrate fractions with items found in the classroom?
Ruler, clock, counters
Which of these number lines correctly compares the fractions: 3/4,3/8,5/6
3/8, 3/4, 5/6
Figure 2 represents a __________ of Figure 1
translation
Which of the following are the most comprehensive options for the students to apply the central measures of tendecy to creating charts and graphs?
Frequency tables,dot plots, stem and leaf plots
Ms. Senath teaches math to a diverse group of students in her fourth-grade class, some of them with learning disabilities. It is important for her to remember when presenting math instruction to her students that —
She should teach math concepts from concrete to the representational to the abstract
A first grade teacher is assessing student ability to apply strategiesto add numbers up to 20. The teks list four strategies students......which of teh following is not a strategy
ten frame
When developing the learning goals to include assessment, Mrs. Jones would be wise to include time for which of the following
Reevaluation of instruction
Which steps would most effectively solve for partial product
Solve the problem by multiplying......
Which of the follow is not proper way to denote multiplication
x9
which of teh following is not an extension of a coordinate plane
x + y=z
5 in^3 is equal to _________cm^3
81.935
What probability vocabulary would the student need to be exposed to prior to the lesson activity
certain,likely, unlikely, impossible
Ms. Chen first graders......For what could this bar-graph type graph be useful
drawing conclusions and generating and answering questions about the data
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