Core Exam - MATH
What is the solution, if any, to the expression: 1n = ?
1
A store is having an end-of-the-year computer sale. What is the total cost of a discounted computer system (i.e., computer, monitor, and printer)? Computer - $1800 discount: 33.3% Monitor - $360 discount 25% Printer - $100 discount 20%
1,550.60
The area enclosed by the rubber band can be calculated by using which of the following expressions?
1/2 bh
Which of the following answer choices is divisible by 6?
12960
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 in a fourth-grade class are working with geoboards. Each geoboard has a grid drawn on it and a peg at each intersection of the grid. Students stretch rubber bands around the pegs to create shapes. One student's shape is shown below. The teacher shows the student how to add the squares and fractions of squares enclosed by the rubber band to count the total number of squares within the triangle. This activity would bestpromote the student's understanding of which of the following geometry concepts?
B.Area
The fourth grade teachers at XYZ Elementary School have planned the next three units in the math scope and sequence. During their planning time, the teachers set learning goals, developed the delivery of the lessons and designed the assessments. They delegated responsibilities for preparing copies of needed materials and set deadlines for when assessments needed to be graded. Which of the following would need to take place to determine if goals were met?
Reevaluate the learning goals and delivery of lessons to determine if the students met the goals through the assessments.
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
Mathematics revision and reform is an ongoing debate to reach a conclusion as to what is "best practices" to improve mathematics education. "It is clear that the work of reform requires large investments of time and energy in order to enact critical change in mathematics education" (Ellis, Berry, 2005). What is one way teachers can work towards reform in mathematics education?
Teachers can design learning environments to allow for mathematical discussion and the connection of mathematical ideas.
According to National Council Teachers of Mathematics, "technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Teachers' attitudes play an important role in using technology in teaching and learning mathematics". Which of these would NOT be an effect of technology on math curriculum?
Technology will make math less important.
The students in a kindergarten class will collect data about the number of children in each classmate's family. The teacher will provide the students with a chart listing each student's name and a blank for the student to write the number in each family next to each name. The teacher will then compile the information the students collected from each other, demonstrate how to sort the data and guide the students through creating a picture graph to show how many children are in each child's family. What might be the goal of this activity?
The goal is for students to take ownership of their own learning and investigate to gather information.
Third grade students at ABC School are asked to classify and sort three-dimensional figures according to their attributes and characteristics. Students are given nets to fold and explore the shapes composing each three-dimensional figure. How would using a net as a manipulative help students classify three-dimensional figures?
The nets would allow the students to see the figure decomposed and be able to label the faces, edges and vertices.
The width and length of a rectangle are whole numbers different from zero. Which of the following statements about the rectangle must always be true?
The perimeter is an even number.
Ms. Jones, a fourth-grade teacher, gave her students the task below. Pat and her sister returned home 2 hours 45 minutes after they had left to see a movie. They returned home at 4:30 p.m. What time did they leave for the movie? 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. Not knowing where to begin, the students began to urge her to give them some help. Wanting them to feel successful and stay engaged, Ms. Jones pointed out to the students that the problem involved subtracting from the time Pat and her sister got home the minutes and hours they were out. She told her students that they needed to convert hour to minutes when subtracting minutes, and that there are 60 minutes in an hour. 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.
Mrs. Jones' students are using principles of inductive reasoning to solve for missing numbers in patterns. Mrs. Jones gave her students the pattern below and asked them to complete the pattern. What might a student reason in order to apply deductive reasoning to complete the pattern?2, 4, 8, 16, 32, 64, ____
I can see the pattern increases, so I must need to add or multiply. If I add 2+2, it equals 4, but if I add 4+2, it equals 6. So, I can multiply 2x2=4 and 4x2=8. The pattern is to multiply by 2.
While learning division facts, the third grade students in Mrs. White's class are learning divisibility rules as they apply to solving problems. The students want to solve 256/4. Use the drop down menu to determine the divisibility rule they should apply to this problem.
If the last two digits are divisible by 4"
The third graders in homeroom 302 are working collaboratively to find the perimeter of the school's garden to determine the number of feet of edging they will need to put a border around one section of the garden. The picture of the garden is shown below. Complete the formula for the perimeter.
P = 2 (12) + 2(5) = 34
In order to push the students to a higher level of thinking, 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.
Which method below does not define a function?
Passes the horizontal line test.
A second grade teacher introducing quadrilaterals to the class has asked the students to apply logical reasoning to justify and prove why a geometric shape is a quadrilateral. Which of the following would NOT be a generalization or justification that a geometric shape is a quadrilateral?
It always has four right angles.
Mr. Grant wants his fourth-grade math students to learn to work collaboratively, to discuss alternative approaches to solving tasks, and to justify their solutions. Students are grouped in pairs and Mr. Grant gives his students the following task: Express the ratios below in the lowest forms: 15/25, 18/6 , 9/36, 18/15 Which of the following best describes the level of student engagement expected with the given task?
It will not engage students in high level forms of thinking.
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
The students of Mr. Smith's third grade class are studying patterns and how they relate to implicit and explicit rules, as well as, solving for missing numbers. The students are solving for the empty places in the pattern below. Use the drop down menu to identify the rule.{ 88837, 12691, 1813, 259, 37, ... }
The rule in the pattern is divide by 7
First grade students are exploring probability in the context of marbles in a bag. The teacher selects three red marbles and six blue marbles to place in the bag. The teacher shows the marbles to the students and asks them to consider if she places all the marbles in the bag, what the probability, or likelihood, is she will pull out a blue marble. The class will make a chart of the number of times she pulls out a blue marble or red marble and record their findings on a class T-chart. 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, and makes the concept more tangible and real for the students, and, to model with correct vocabulary (of the concept) introduces the student to mathematical language needed as they continue to explore concepts throughout mathematics.
The students in homeroom 304 were asked to bring in illustrations of real-world forms of symmetry in tessellations. Students had previously learned about symmetry and tessellations through visual representations of honeycombs. What does the teacher understand about the importance of students finding other examples of tessellations in the world around them?
The teacher understands the importance of students being aware of their environment and applying what they are learning in the classroom to what they experience and see around them.
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.
Mrs. Williams' kindergarten students are collecting data about the first graders' favorite color of chocolate coated candies. What conclusions can be drawn from the graph below?
There are 40 first graders who like red chocolate coated candies. There are 50 first graders who like orange and yellow chocolate coated candies.
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?
There are four quadrants in a coordinate plane, and quadrant 2 and quadrant 3 are positive.
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.
After a lesson in finding the area and the domain of the length of a side of a rectangle given the perimeter of the rectangle, the teacher finds that almost all the students have answered the following question this way. What would be the best approach for the teacher to respond to the answers?
Congratulate the students on their efforts of critical thinking through a tough question and their ability to calculate the area correctly. Follow up with a mini lesson on multiplication property of zero. Let students work in pairs to analyze if they want to change their answer for the domain.
An early childhood teacher is instructing students on classifying shapes according to their attributes. Which characteristics, using formal and informal language, might the teacher introduce to the students as a way to classify a two-dimensional shape?
sides, corners, can it roll
Which factor would indicate the importance of teaching rounding and estimation within mathematical computation?
to make sense of problems and persevere in solving them
Vickie is having her kindergarten class match each star with one moon by drawing one line from a star to a different moon. What type of matching relationship is this task?
transformations
Mrs. Jones' first graders are learning how to write equations. The students have previously learned to write equations with addends and minuends, but today, they are learning to write an equation when an addend is missing. For missing values, Mrs. Jones has introduced that a symbol can be put in the place of a missing addend. What is the proper mathematical term for the symbol in this equation? 13 + __ = 18
variable
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)
Which of the follow is NOT a proper way to denote multiplication?
x9
Which of the following would not be an important indicator towards learning place value within the Base Ten number system?
adding by ones
Which basic operation(s) has commutativity?
addition
In early grades, probability is described as a likelihood of something occurring, or a chance that it will occur. Second grade students were placed into groups to determine the probability of rolling certain numbers or types of numbers on die. What probability vocabulary would the students need to be exposed to prior to the lesson activity?
certain, likely, unlikely, impossible
Which of the following is NOT a prerequisite for children to recognize patterns?
compare sets
Fifth graders at Smith Elementary were introduced to number bonds as first graders. Which of the following, when applied to fifth grade concepts, would relate back to number bonds?
diagrams
The teacher is introducing ways to chart and graph the measures of central tendency. Which of the following are the most comprehensive options for the students to apply the central measures of tendency to creating charts and graphs?
frequency tables, dot plots, stem-and-leaf plots
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
Mr. Williams is preparing a lesson on counting money with coins and bills for his second grade students. He has set up a store in his classroom whereby students will shop for school supply items then pay for them with play money. Mr. Williams is hoping the students will learn to make change correctly by applying the concept to a real-world situation which many of his students experience in purchasing their own school supplies. Which of the following instructional strategies could Mr. Williams be hoping to achieve with this lesson?
math language and discovery activity
Congruent triangles can be used to explore geometric relationships. Which of the following is NOT representative of a position of congruent triangles?
mirror
Learning to skip count forward in lower grades is preparation for which of the following mathematical operations?
multiplication
The kindergarten teacher has introduced three-dimensional shapes to the class. The teacher brought in common examples of each shape for the students to classify according their attributes. In order to create a visual reminder to help the students with recall, the teacher created an anchor chart to classify each object. Which attributes might the teacher have included on the anchor chart?
number of edges, number of vertices, number of faces
Jamie is reading the story of Goldilocks and the Three Bears with her pre-kindergarteners this morning. She asks the children the following questions: What was the first thing that Goldilocks did when she came into the bears' house? What was the second thing that the bears noticed when they returned to the house? In what order did Goldilocks sit in the bears' chairs? What skill do you think Jamie is integrating into the discussion of this story?
ordinal numbers
Which choice represents an element whose only factors are itself and 1?
prime numbers
The greatest benefit of providing elementary students with mathematical tools such as geoboards is that these tools —
provide students with visual representations that promote their conceptual understanding.
The 3rd graders in Mr. Roberts' class were asked to solve the following problem: Bobby has two ten dollar bills. He buys seven lollipops for $2 each. How much money will Bobby have left after his purchase of the lollipops? 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.
A teacher has students working in groups of three to solve the following equation. She provides each group with two quarters, two dimes, and two nickels. Also, she explains that negative amounts would mean you owe the amount. −0.25 + ? = −0.15 The teacher is trying to get students to understand the concept of _________________.
Adding a positive and negative
Many cultures have influenced and contributed to mathematics as we know it today. Which four cultures have had the most impacts that are still relevant today?
Ancient Greece Babylonia India Ancient Egypt
A quilt is made using the following pattern. This is an example of
2-dimensional geometric model
Cars A and B travel in the same direction for a 2-hour period and the distance they travel is represented in the graph above. If each car continues to travel in the same direction and at its current speed, what will the distance between them be after 3 hours?
60 miles
Mrs. Granato would like to introduce her students to careers and professions which use math in the workplace. She has made arrangements for a banker to come in and discuss with her class the many roles a banker has within a bank. Which of the following TEKS might Mrs. Granato be able to apply to this lesson? Click each TEK below which could apply to this lesson.
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
What is another way to say average in mathematics?
Mean
Students are having a hard time understanding how to add a known constant with an unknown value, so the teacher borrows two beakers and brings two identical glass bowls to class. She fills one beaker with 200 ml of water and the second beaker with 300 ml of orange juice and pours in the same bowl. Students understand there is 500 ml of water/orange juice mixture in the bowl. Now, the teacher puts masking tape around the second beaker, so the scale is not visible. She fills the first beaker with 200 ml of water and the second beaker with an unknown amount of grape juice and pours both beakers in the 2nd bowl. It is obvious that the second bowl has more than the first bowl. So, students determine the fluid in the second bowl is _______ the fluid in the first bowl. After some discussion and coaching from the teacher, the students determine the unknown will be represented by x. The teacher has one of the students write a big "x" on the masking tape. Now, the teacher pours the 200 ml from the bowl back in beaker 1 and the rest back in the beaker with the masking tape. The teacher repeats the steps. She pours the 200 ml in the glass bowl and has students write down on a piece of paper "200 ". Next, she pours the unknown amount from the beaker labeled with "x" in the bowl. She has students write down how much more has been poured in the bowl. About ¾ of the class understand that x-amount of fluid was added to 200 ml making the total fluid in the 2nd bowl 200 ml + x ml. The teacher is trying to teach ______ in this lesson.
> the connection between math and science
Is the graph of a circle a function? Describe why or why not.
No. It does not pass the vertical line test.
A class of second graders is learning about the properties associated with lines in regards to measurement and length. The students are learning to define geometric terms by their proper definitions. 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.
Given two even integers, a and b, determine what could be the least common multiple (LCM)?
ab/2
A fifth grade math teacher is introducing different methods of payment within the financial literacy curriculum. Select all that apply as payment methods.
Check Credit Card Debit Card Electronic methods life AFT and EFT
The teacher has designed several stations within the classroom for students to practice measuring objects based upon length and distance. Some of the stations require the students to use standard units of measurement and other stations require students to use non-standard units of measurements, such as paper clips. The teacher will monitor and move about the classroom while students work in small groups to solve the task cards at each station. What approach to learning is the teacher implementing in this lesson?
Constructivist theory
While introducing two -digit addition to a second grade class, the teacher first models adding a problem with Unifix cubes to demonstrate the relationship between tens and ones. The next day the teacher models adding a problem with base ten blocks and has the students draw and write the problem in their math notebooks. On day three, the teacher moves to a more abstract approach to adding two-digit numbers. What would be the next step for the teacher in this lesson series?
In order to support the previous days' lesson, the teacher should model adding two-digit numbers by drawing base ten blocks to show the steps to adding, then have the students solve some problems on their own by drawing the base ten blocks to solve additional two-digit addition problems.
While introducing two-digit addition to a second grade class, the teacher first models adding a problem with Unifix cubes to demonstrate the relationship between tens and ones. The next day the teacher models adding a problem with base ten blocks and has the students draw and write the problem in their math notebooks. On day three, the teacher moves to a more abstract approach to adding two-digit numbers. What would be the next step for the teacher in this lesson series?
In order to support the previous days' lesson, the teacher should model adding two-digit numbers by drawing base ten blocks to show the steps to adding, then have the students solve some problems on their own by drawing the base ten blocks to solve additional two-digit addition problems.
Which of the following is not a reason as to why it is important that students be given freedom to solve a mathematical problem in more than one way?
The teacher has the correct way to solve each mathematical problem, and it saves time if the students will solve it the way the teacher instructs.
Mrs. Case is arranging her kindergarten classroom to look like a small grocery store. When students arrive for the day, they will be given a job to shop for items on a list or to be a cashier in the store. After a while, students will switch roles. What might be the goal of Mrs. 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.
Ms. Ramirez and her first grade students will be classifying polygons by their attributes. She plans to engage the students by arranging stations around the classroom for students to rotate through and practice working with the polygons. 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 a small group but to also check in on the other stations
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. Students may work with one partner or alone but must design a creative way to present the need for coordinate grids in real-world situations. 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
Nissa and Alex are picking apples in the orchard. They had picked enough apples to fill two buckets. They knew they had picked 53 apples and that there were 32 apples in the second bucket. Which expression will help Nissa and Alex determine how many apples are in the first bucket?
? + 32 = 53
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 1+1 1+2+1 1+3+3+1 1+4+6+4+1
1 + 6 + 15 + 20 + 15 + 6 + 1
Amber's dog, Mac, eats approximately $85 of dog food in 2 weeks. How much will Amber spend on dog food in a year?
$2210
The 1st grade students, including ELL students, at Rice Elementary will be assessed over their understanding of U.S. coins and the value of each coin. During class instruction, all students were able to concretely work with play money to make connections with coins and values. The teacher must determine the best way to assess students over the values of the U.S. coins. Which would be an appropriate method to do so?
Provide pictures of each U.S. coin and have students match the picture with the value of the coin.
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 the concrete to the representational to the abstract.
A first grade teacher is assessing students' ability to apply strategies to add numbers up to 20. The TEKS list four strategies students should learn in first grade. Which of the following is NOT one of those strategies?
ten frame
The students in Mr. Campbell's first grade class were given a picture of different insects and asked to graph the number for each insect in a bar graph. The students were then instructed to draw conclusions from the graph. Which of the following could be a conclusion Mr. Campbell would like for the students to be able to derive from the graph?
There are more butterflies than bumblebees and more dragonflies than ladybugs.
The students in a kindergarten class will vote between the zoo and the space center for the destination of their next field trip. The teacher has placed two bowls at the front of the room and given each student one marble to place in the bowl with the label of the destination he or she will choose. Students may only vote once. Which TEK would be best supported by this activity?
collect, sort, and organize data into two or three categories
Students are using pattern blocks shaped as congruent equilateral triangles to construct fraction problems. Which of the following fractions does the parallelogram represent?
4/7
Walter looks forward to Fridays because his teacher plays his favorite math game during the math period. She gives the class a number, and the students write an expression to equal that number. The object is to use some unusual methods to calculate the number because the class wants to get as many different answers as possible. Today the teacher gives the number 24. Which of the following is the correct expression to equal 24?
60 ÷ 3 + 6 − 2 • (−1^0)
What is the probability that both a couple's last two children will be girls?
1/4
A couple has five grandchildren about the same age. The couple found a large box and put 13 packages in this box. All of the packages were wrapped in either Santa or Snowman paper. At Christmas, each grandchild was allowed to draw two packages from the large box in succession without replacement. When the box came to the 5th grandchild, it had 3 packages wrapped in Santa paper and 2 packages wrapped in Snowman paper. What is the probability that this 5th grandchild will draw a package wrapped in snow paper on the second draw?
2/5 x 1/4 + 3/5 x 2/4
What is the missing number? 4, 12, 36, 108, _____, 972
324
During math work stations, the students are to use the Math Talks poster to guide their thinking in solving the given problems. As the teacher walks around the room helping different students, the teacher hears Johnny ask Joe how he solved the problem of five times nine. Which response from Joe may have appeared on the Math Talks poster as a way to explain his thinking?
B.I multiplied five times nine by counting by fives nine times.
The kindergarten teacher has introduced three-dimensional shapes to the class. The teacher brought in common examples of each shape for the students to classify according to their attributes. In order to create a visual reminder to help the students with recall, the teacher created an anchor chart to classify each object. Which attributes might the teacher have included on the anchor chart?
B.number of edges, number of vertices, number of faces
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 students in homeroom 232 are exploring equivalencies when an addend or minuend is missing. The teacher has given the students the following equation:18 +__?__= 25 The teacher's goal is for the students to be able to explain how to solve this problem. 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 you explain what would make this equation true?
Which set(s) does the number 3 belong to? l. whole numbers ll. integers lll. rational numbers lv. irrational numbers
I, II and III
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
Joelle and her friends are planning to visit the zoo in the neighboring town. They know the price of each student ticket is $5 and each adult ticket is $7. If Joelle and 7 of her friends visit the zoo with two parents, what will be the final costs of the zoo tickets? What method could the student use to most efficiently solve this problem?
Multiply five times eight then multiply seven times two then add the two products together.
Below are ways teachers can connect mathematics and other disciplines. Drag and drop the math concept to match with a related discipline of learning.
Music - Patterns and Symbols Art - Tessellations Science - Mass Social Studies - Changes in population Businesses - Budgets
The use of manipulatives and technological tools within the discipline of mathematics assists students and teachers to explore and identify mathematical concepts and relationships. Click in the boxes of each column to indicate which manipulatives and tools could be used offline and online.
Offline - Base Ten Blocks -Calculator -Protractor Online -Base Ten Blocks -Calculator -Interactive Whiteboard -Protractor -Web-based Videos
Mr. Jansen's second-grade students have been working on addition and are now ready to begin learning two-digit subtraction. To introduce this new unit of study, he first has students work on addition problems they are familiar with and then follows up by demonstrating to them how those problems are related to subtraction.Mr. Jansen has been debating whether or not he should allow his students to use calculators to do their math. Some of his students are learning disabled. 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.
A teacher is planning a lesson on addition with early childhood students. In order to incorporate concrete models into the lesson, the teacher will use cubes of two different colors. 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
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 for students to place the crackers inside the rectangles in a way that will fill each rectangle. Students will work in partners to fill each rectangle and record the amount of crackers it takes to fill a rectangle. The number of crackers will indicate the area of the rectangle. By exploring in this way, the teacher is not only providing a means for exploration but also a way for students to enrich their learning experience. 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 is introducing comparing whole numbers in terms of greater than and less than. The teacher brings to class ads from two different grocery stores. The teacher instructs the students to find three items that appear in each ad and compare their prices. 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.
Second graders will be introduced to fractional parts through the use of shaded regions. The teacher will introduce that the more fractional parts used to make a whole, the smaller the part, and the fewer the parts, the larger the part. The teacher will guide students to apply the concept to halves, fourths and eighths. In order for students to see the difference in the fractional parts, 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.
In a third-grade math class, 75% of the students failed the assessment over probability and data collection. In presenting the lessons, the teacher had introduced the concepts, assigned worksheets to be completed at school and at home and had assigned the students a few games to play in class. However, when the teacher observed the students completing the assessment and made observations as to why the majority of the students failed the test, the teacher noticed most of the students applied the incorrect plots to charting the data provided in the word problems. 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.
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. The class has been divided into groups and given a list of items to purchase with a set budget. The students are to shop the store and use mental math with rounding to assess if the budget they have been given is adequate to purchase the needed items. The students have a set amount of time to complete the assignment. Which mathematical processes would be applicable in this activity?
Rounding to the whole number, addition of whole numbers, subtraction of whole numbers
Mr. Williams teaches a 3rd grade math class specifically for English Language Learners. His students are representative of four different cultural and country backgrounds. Some of the students do not currently speak English fluently. While this does present a challenge for Mr. Williams when communicating with the class as a whole, he designs his instruction in such a way that each student feels valued and understood. Which approach may be most beneficial for Mr. Williams' students as he assesses them over a current concept?
Scaffold the assessment to the level of conceptual comprehension- concrete, semi-abstract, abstract- to assess each student's ability and knowledge of the concept.
In teaching geometric concepts with early childhood learners, it is important to teach developmentally appropriate vocabulary alongside the mathematical language? Match the developmental vocabulary with the correct mathematical language.
Shapes - Polygons Squares and Rectangles - Quadrilaterals Diamond - Rhombus Ball - Sphere Circle - Closed Figures
Given the assignment of converting 215°F to Celsius, a 6th grader comes up with an answer of 101.7°C. 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.
Students learn from what they do and the process they go through to acquire knowledge. Their learning of mathematics impacts society and culture. What theory of learning would this statement support?
Situated Learning theory
Calculators, base-ten blocks, attribute blocks and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Attribute blocks is a type of manipulative most effectively used to teach which of the following sets of concepts?
Sorting, classification, investigation of size, shape, color, logical reasoning, sequencing, patterns, symmetry, similarity, congruence, thinking skills, geometry, organization of data.
Base-ten blocks, attribute blocks, Cuisenaire rods and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Cuisenaire rodsis a type of manipulative most effectively used to teach which of the following concepts?
Sorting, ordering, counting, number concepts, comparisons, fractions, ratio, proportion, place value, patterns, even and odd numbers.
Students were assigned to work in groups of two to investigate probability and its properties as it relates to flipping two coins. Prior to flipping the first pair of coins, partners were to predict the outcomes of 10 flips. Pairs were assigned to flip two pennies and to record their findings of HH, HT, TH or TT in a frequency chart. The teacher observed some students skipping the prediction step. 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 before they move on to flipping the coins and collecting the data; then observe them making the predictions and working through the flipping part of the activity.
According to the TEKS, third grade students are expected to determine the value of a collection of coins and bills. The teacher has written $7.62 on the board and asked students to explain what bills and coins they would use to show this amount. 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.
Third graders have been exploring finding the area of regular and nonregular polygons, as well as, writing the area as a fraction of the whole. Students were given two rectangles drawn on grid paper and asked to decompose each rectangle into two shapes with the same area but not the exact same shape. What explanation may the students have given to know the areas are equal?
Students may have decomposed rectangle A vertically and rectangle B horizontally; whereas rectangle A would have 6 rows of 2 to represent ½ and rectangle B would have 3 rows of 4 to represent ½.
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. Students were given the following the image from the blueprint. 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.
Mr. Jacobs' fifth graders will work in small groups to solve addition and subtraction of fractions with like and unlike denominators. 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.
Using probability to describe the outcome of simple events, the teacher brought to class a box of 24 popsicles in four colors. In the box are eight red popsicles, six orange popsicles, four green popsicles and six purple popsicles. How would the class describe the simple event of the teacher selecting one green popsicle from the box?
The simple event of selecting one green popsicle is the number of favorable outcomes over the number of total outcomes; thus, the probability would be
First grade students are exploring probability in the context of marbles in a bag. The teacher selects three red marbles and six blue marbles to place in the bag. The teacher shows the marbles to the students and asks them to consider if she places all the marbles in the bag, what the probability, or likelihood, is she will pull out a blue marble. The class will make a chart of the number of times she pulls out a blue marble or red marble and record their findings on a class T-chart. 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, and makes the concept more tangible and real for the students, and, to model with correct vocabulary (of the concept) introduces the student to mathematical language needed as they continue to explore concepts throughout mathematics.
A teacher has arranged the classroom into stations so that students can work in groups of three or four to apply measuring with rulers, yardsticks, meter sticks and measuring tapes to the nearest marked unit. Students will be given an expectation of what to measure and a length of time to spend in each station. Students are to estimate each object prior to finding its actual measurement then compare the estimation and actual measurement. What should the teacher be doing while students are working in groups?
The teacher should be assessing each group, observing students as they problem solve together, and ask probing questions to the groups to guide them to think deeper.
Fifth graders learning about coordinate planes and graphing ordered pairs were put into teams of two to design a board game in which their fellow classmates would be able to play to practice graphing and finding the x-axis and y-axis. 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.
Johnny is solving the following word problem with a classmate. Elyse is 26 years younger than her mom. If Elyse's mom is 32, how old is Elyse? The students find the solution to be 26. How could Johnny and his classmate 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.
Using the Present Value Formula, students have calculated a house payment for a loan set up on an annuity. The principal is $127,000 and the monthly payments are $583.56. The students want to know how much interest over the period of the note (30 years) will accrue. They decide the first step is to calculate the total amount to be invested in the house. For this, they determine the following equation should be used. Payment amount x Number of payments = Total amount invested What should the next step of the algorithm be?
Total amount invested - Principal
Mrs. Jones is planning learning goals for her kindergarten students as she begins a series of lessons on patterns. Mrs. Jones will present her class with opportunities to learn about patterns in a variety of ways. She will create and use representations to organize, record and communicate the mathematical ideas behind patterns. Following the series of lessons, Mrs. Jones will assess her class on the skills and knowledge that have been taught. When developing the learning goals, it would be wise for Mrs. Jones to include which of the following?
reevaluation of instruction
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
First graders are applying skip counting as they count to 100. The teacher wants to explore common items for the students to use with skip counting. For skip counting by 5s, the teacher will have the students trace their hands and number their fingers then glue the hands on a large poster board to display the number of hands with five fingers it would take to reach 100. What are some things the teacher could use to teach skip counting by 2s?
socks, shoes, feet
Determine the choice that does not relate to the following: 10x + 5
solve for the value of x
A class of second grade students are classifying two-dimensional polygons. Students are given a rectangle and asked to decompose it to form new two-dimensional polygons. Which of the following identifies the geometric parts that could NOT be formed from decomposing the rectangle?
two congruent rectangles, 1 circle
Students in first grade are expected to organize data to make it useful for interpreting information and solving problems. Ms. Chen has designed a project for her first graders to collect data from the second graders about favorite ice cream flavors. Ms. Chen has provided three options of flavors for students to choose from. The first graders will interview the second graders and ask their favorite flavors then bring the data back to class. Once the data arrives back in class, 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
Students in the second grade class at Lovett Elementary are exploring properties of U.S. coins and bills. The teacher knows to help students make clear connections with the play money in class and real money they would use at a store that the lessons and activities need to be applicable to a real world situation. Which of the following situations would be the most applicable for the students?
for students to shop in the "class store" and count out the money needed to make the pretend purchases
Students normally receive either a 0 or 100 for an attendance grade each day based on whether they are present or not. This particular day the teacher decides to give the students a quiz after a lesson has been presented and all students who take the quiz receive a grade of 100 for participation that day. The teacher plans to look at the quizzes to determine the level of comprehension of the topics taught that day, mark corrections, hand back the quizzes to the students the next day, and adjust the contents taught the next day based on the results. What type of assessment techniques is the teacher utilizing?
formative
In preparing students to be successful in problem solving with word problems and given tasks, the TEKS state five parts which should be included in a problem solving model. These parts are best implemented in conjunction with one another but may stand alone as each part is taught and introduced. Four of these parts are: analyzing given info, determining a solution, justifying the solution and evaluating the problem-solving process and the reasonableness of the solution. Which of the following would be the fifth part of this process model?
formulating a plan or strategy
The students in a third grade class are struggling with learning the conversions within the U.S. customary system of measurement as they apply to capacity. The teacher has designed an interactive lesson whereas students will have the opportunity to practice applying the conversions. Which of the following units would the teacher have available for students to measure capacity?
gallon, quart, pint, cup, ounce
A second grade teacher has asked his students to classify a set of polygons by their attributes. Which of the following attributes might his students use to classify the polygons?
number of sides and number of angles
Mr. Brown introduced his class to solving for missing angles within triangles. He provided his students with graphic representations of triangles and asked them to solve for the missing angle. For which representation of the triangles is Mr. Brown asking his students to solve?
numeric
ABC ISD is improving its curriculum needs through technology and hands-on experiences. Which of the following would provide a hands-on experience of being able to manipulate, rotate, transfer, and decompose three-dimensional shapes?
visual media
Personal financial literacy was added to the TEKS in 2012 so that students might learn to apply "mathematical process standards to manage one's financial resources effectively for lifetime financial security." (TEKS, 2012) Which of the following would NOT relate to one's financial security?
volunteer jobs
Given the task of computing two consecutive even numbers whose sum is 50. Let xrepresent one number. Determine the choice below that should represent the second number.
x + 2