Pre-Test
A student is tasked with selecting two cards with replacement from a fair poker deck of 52 cards. Which option demonstrates correct student reasoning about possible results of this experiment? Choose 1 answer a) "Getting two kings is just as likely as getting two 10s." b) "If you get a red card on the first pull, you're more likely to get a black card on the second pull." c) "With two draws, there is a 1 in 5 chance of getting a red card both times; the three possible outcomes are two red, two black, and one red and one black. " d) "Since there are 52 cards in the deck, there's an 8 in 104 chance that I get 5 on both draws."
a) "Getting two kings is just as likely as getting two 10s."
Which two demonstrate correct student geometric reasoning? Choose 2 answers a) "It seems that, in triangles, longer sides are opposite larger angles." b) "If I double the sides of a square, then the area will be doubled as well." c) "Since this square is also a rectangle, I can conclude that rectangles are also squares." d) "Three numbers x, y, and z that form a Pythagorean triple satisfy x 2 + y 2 = z 2. They must also satisfy x + y = z." e) "I have measured many different circles' circumferences and diameters, and the ratio of these always seems to be the same number. I predict that if I measure more, the ratio will have the same value."
a) "It seems that, in triangles, longer sides are opposite larger angles." e) "I have measured many different circles' circumferences and diameters, and the ratio of these always seems to be the same number. I predict that if I measure more, the ratio will have the same value."
Which two instructional strategies support a classroom environment that encourages mathematical communication? Choose 2 answers a) Include assessment opportunities for students to explain their thinking b) Tell students a problem is easy so they will be confident they can solve it c) Call only on volunteers during class discussion to decrease student anxiety d) Use time when students present their ideas to assess the correctness of their answers e) Restate student created terminology by using precise mathematical language when introducing vocabulary.
a) Include assessment opportunities for students to explain their thinking e) Restate student created terminology by using precise mathematical language when introducing vocabulary.
Which process has a student demonstrated when they use multiple representations? a) Moving from instrumental to relational learning b) Moving from fundamental to relational learning c) Moving from relational to fundamental learning d) Moving from instrumental to fundamental learning
a) Moving from instrumental to relational learning
Which two statements describe common mathematical learning theories? Choose 2 answers a) New ideas are accommodated in the brain by reworking old ideas. b) New ideas are assimilated in the brain by memorizing procedures. c) New ideas are made accessible through peer and teacher support. d) New ideas are built through teacher modeling of efficient algorithms. e) New ideas are developed separately from classroom culture or setting.
a) New ideas are accommodated in the brain by reworking old ideas. c) New ideas are made accessible through peer and teacher support.
Which two tools can be used to teach a lesson on fractions? Choose 2 answers a) Tangram b) Compass c) Cuisenaire rods d) Isometric drawing tool
a) Tangram c) Cuisenaire rods
Which two strategies could be part of a lesson plan that uses a think-aloud strategy rather than peer-assisted learning? Choose 2 answers a) The teacher discusses alternative methods for problem solving. b) Students use tools to increase the understanding concept. c) The teacher talks through the steps of a solution, identifying the reasoning at each step. d) Younger students work with older students who have more sophisticated ideas of the concepts.
a) The teacher discusses alternative methods for problem solving. c) The teacher talks through the steps of a solution, identifying the reasoning at each step.
A lesson for fifth-grade students focused on solving the following and other similar equations: 3x + 7 = 18 14 = 2x - 8 5(x + 1) = 20 Which equation should the teacher use to assess these students' understanding of the lesson? a) -4x + 3 = 12 b) 3(x - 2) = 15 c) x + 6 = 14 - x d) 14 - 2.5x = 18
b) 3(x - 2) = 15
Students are learning to add and subtract three-digit numbers. Which two student activities promote communication about their mathematical thinking? Choose 2 answers a) Play a computer game that subtracts three-digit numbers. b) Draw a picture that represents subtracting three-digit numbers. c) Create a story problem that requires adding three-digit numbers. d) Practice adding and subtracting three-digit numbers on a worksheet.
b) Draw a picture that represents subtracting three-digit numbers. c) Create a story problem that requires adding three-digit numbers.
Which two instructional strategies are useful for facilitating effective class and small group discussions about mathematics? Choose 2 answers a) Have students score and grade the work of peers b) Have students compare and contrast solution strategies c) Have students provide the correct answer to each problem d) Have students share alternative problem solving approaches
b) Have students compare and contrast solution strategies d) Have students share alternative problem solving approaches
First-year algebra students are learning how to solve two-step equations. The teacher notices that the students are not using precise mathematical language. Which two instructional strategies should the teacher employ to encourage students to use precise mathematical language when completing this task? Choose 2 answers a) Assign homework exercises to practice mathematical vocabulary b) Model think-alouds for students demonstrating mathematical vocabulary c) Use procedural and conceptual questions using mathematical vocabulary d) Model wait skills to enhance students' metacognition skills and use of mathematical vocabulary
b) Model think-alouds for students demonstrating mathematical vocabulary c) Use procedural and conceptual questions using mathematical vocabulary
A lesson is being designed to address the Communication standard from Principles and Standards for School Mathematics (PSSM). The lesson requires that students write out directions for using fraction bars to model several addition problems. How does this lesson meet the Communication standard? a) Students recognize and use connections among mathematical ideas. b) Students use the language of mathematics to express ideas precisely. c) Students create and use their own measurement units to measure an object. d) Students model physical phenomenon with algebraic equations and appropriate technology.
b) Students use the language of mathematics to express ideas precisely.
A predominantly male third-grade class has several students with moderate learning disabilities. Which instructional strategy would help the teacher provide equitable learning opportunities for this diverse class? a) Emphasize the rote memorization of processes and procedures b) Teach multiple representations of ideas for one problem at a time c) Focus lessons on processes and procedures prior to introducing context d) Maintain authority by keeping instruction and discussion teacher-dominated
b) Teach multiple representations of ideas for one problem at a time
The objective of a lesson is for students to solve word problems involving the multiplication of multi-digit numbers. Although able to solve multi-digit multiplication problems, one student struggles to solve word problems. How can this student's needs be accommodated? Choose 2 answers a) The student practices multiplying multi-digit numbers. The numbers are not presented in word problems. b) The student solves the multi-digit multiplication problems. The teacher models the problem-solving process for the word problem, and then prompts and questions the student. c) The teacher writes the number sentence for each word problem. The student multiplies a single-digit number to find the product. d) The student solves word problems involving the multiplication of multi-digit numbers. The student uses a calculator to multiply the numbers.
b) The student solves the multi-digit multiplication problems. The teacher models the problem-solving process for the word problem, and then prompts and questions the student. d) The student solves word problems involving the multiplication of multi-digit numbers. The student uses a calculator to multiply the numbers.
A teacher asks her students to solve this problem: What is the mean of the numbers 12, 18, 16, 24 and 10? Which two instructional strategies could the teacher use to encourage students to create their own representation of their mathematical thinking? Choose 2 answers a) The teacher demonstrates entering the five numbers into a spreadsheet program and asks students to solve the problem using a spreadsheet formula. b) The teacher asks each student to create a picture to demonstrate how to determine the solution. c) The teacher gives a calculator to pairs of students and asks them to work together to solve the problem. d) The teacher asks the students to work in cooperative groups to create a word problem using the scores and explain to the class how they found the solution.
b) The teacher asks each student to create a picture to demonstrate how to determine the solution. d) The teacher asks the students to work in cooperative groups to create a word problem using the scores and explain to the class how they found the solution.
How does a teacher use a rubric to analyze student performance? a) To determine if a student's response is correct or incorrect b) To assign a score to a mathematical task based on a preset scoring framework c) To determine one framework for scoring that will be used for all mathematical tasks d) To assign a grade to a mathematical assignment based on a preset grading framework
b) To assign a score to a mathematical task based on a preset scoring framework
A student constructed a graph to show how many of a town's residents have completed five different levels of education (elementary school, high school, two years of college, four years of college, graduate school). Which student explanation shows correct mathematical thinking? a) "I used a line graph because it shows how the level of education changes over time." b) "I used a circle graph because it shows the percent of people at each level of education." c) "I used a bar graph because it compares the number of people in each level of education." d) "I used a scatter plot because it compares the number of people with their level of education."
c) "I used a bar graph because it compares the number of people in each level of education."
Which two statements are common misconceptions about place value? Choose 2 answers a) A student concludes 9 - 2 = 11. b) A student concludes 7 + 8 = 56. c) A student writes six hundred three as 63. d) A student writes the expanded form of 32 as 3 + 2.
c) A student writes six hundred three as 63. d) A student writes the expanded form of 32 as 3 + 2.
Which two statements describe learning difficulties that students from diverse groups may encounter? Choose 2 answers a) Students with hearing impairments struggle with organization and self-regulation. b) Students with patterns of low achievement do not benefit from high expectations. c) Students from other countries often solve problems or illustrate concepts differently. d) Students who are English Language Learners (ELL) require more time to solve problems.
c) Students from other countries often solve problems or illustrate concepts differently. d) Students who are English Language Learners (ELL) require more time to solve problems.
During which two activities will students make a mathematical connection to contexts outside the math curriculum? Choose 2 answers a) Students practice writing their numerals using cursive writing. b) Students use base ten blocks to illustrate three-digit numbers. c) Students sort and classify flowers by the symmetry of the petals. d) Students create bar graphs comparing populations of countries in South America.
c) Students sort and classify flowers by the symmetry of the petals. d) Students create bar graphs comparing populations of countries in South America.
A second grade class is learning about the part-plus-part-equals-whole addition model. Their teacher decides to use the common experience of eating in the cafeteria as a context outside the mathematics curriculum to teach this concept. Which scenario exemplifies this addition model? a) Five students are eating lunch together b) Two students finish lunch and go out to recess c) Three students eating lunch are joined by two more students d) Three students are eating lunch while two students are at recess
c) Three students eating lunch are joined by two more students
What is an appropriate use of manipulatives from web-based technology in mathematical instruction? a) A teacher shows a website and instructs the students to follow along and model. b) A teacher shows a website and asks students to talk with each other to see how each thinks. c) A teacher shows a website and makes it accessible for school or home use for further exploration. d) A teacher shows a website and demonstrates how to effectively interact with virtual manipulatives.
d) A teacher shows a website and demonstrates how to effectively interact with virtual manipulatives.
In a sixth-grade math class, students are reviewing operations involving fractions. The teacher wants to use an instructional strategy that will encourage students to build on another student's prior description about how to add two fractions. How should the teacher do this? a) Ask other students to restate the explanation as a question b) Ask other students what they thought of the first student's description c) Ask other students to restate the first student's description using their own words d) Ask other students to add to and provide examples of the first student's description
d) Ask other students to add to and provide examples of the first student's description
The students in a class studied polygons, including classifying polygons as concave, convex, and regular. Which performance task will effectively assess understanding of what was taught? a) Draw a convex polygon, a concave polygon, and a regular polygon and then describe the characteristics of each b) Given a group of polygons, classify them into three groups and then describe the characteristics of the polygons in each group c) If possible, draw a polygon that is both convex and regular and then, if possible, draw a polygon that is both concave and regular d) Given a variety of polygons, arrange the polygons by concave, convex, or regular and then describe the characteristics of each.
d) Given a variety of polygons, arrange the polygons by concave, convex, or regular and then describe the characteristics of each.
During the basketball season, a player scored 12, 14, 11, 17, 21, 18, 17, and 12 points in the first eight games. Which representation of the data shows the player's points scored in each game? a) Bar graph b) Histogram c) Circle graph d) Stem-and-leaf plot
d) Stem-and-leaf plot
Two students worked together to compute 3/4 - 5/8. Student A thinks the difference is 1/0 and student B thinks it is 1/8. Which teacher response is appropriate to evaluate conceptual understanding? a) "Student A, will you please explain the process you used?" b) "Student A, division by 0 is not possible. Will you please try again?" c) "Student B, your answer is correct. Will you please explain it to Student A?" d) "Student B, will you please show Student A the process of finding a common denominator?"
a) "Student A, will you please explain the process you used?"
Which two strategies teach for understanding of mathematics? Choose 2 answers a) Allow use of a variety of manipulatives to model the problem b) Encourage use of verbal descriptions in problem-solving activities c) Reteach using a standard procedure to solve all problems d) Correct student errors by solving the problem using the correct method
a) Allow use of a variety of manipulatives to model the problem b) Encourage use of verbal descriptions in problem-solving activities
A teacher wants his students to communicate mathematically outside of his classroom. He gives a homework assignment that requires the students to participate in mathematical discourse. Which technology could the teacher assign the students to use from home to meet this objective? a) An Internet mathematics forum b) Dynamic geometry software c) An online library of math journals d) Graphical presentation software
a) An Internet mathematics forum
Which activity could be used to make a mathematical connection within a mathematics curriculum when teaching a unit on basic probability? a) Demonstrate how probabilities can be displayed in a pie graph b) Use manipulatives to calculate basic probabilities c) Explain how probabilities are related to real-world decision making d) Have students create journal scenarios representing basic probabilities
a) Demonstrate how probabilities can be displayed in a pie graph
Which two resources can help a student visualize similar triangles? Choose 2 answers a) Grid paper b) Concept map c) Online discussion d) Dynamic geometry software
a) Grid paper d) Dynamic geometry software
A first-grade class includes students who lack motivation and students with mild learning disabilities. Which two instructional strategies would meet the needs of this group of students as they study math? Choose 2 answers a) Help transitioning from a problem to a particular representation b) Opportunities to discuss problems and ideas with other students c) A separate learning environment with students of similar ability d) Peers to review and correct their answers
a) Help transitioning from a problem to a particular representation b) Opportunities to discuss problems and ideas with other students
Students are working in groups on the following problem: Teresa has twice as many marbles as Patrice. Together they have 36 marbles. How many marbles does each girl have? Mena states, "Teresa has 12 marbles and Patrice has 24 marbles." How should the teacher respond to promote an understanding of Mena's thinking? a) Mena, can you explain how you got your answer? b) Can someone show Mena why her answer is wrong? c) Mena, you have the right numbers but in the wrong order. d) Can someone explain to me why Mena's answer is right or wrong?
a) Mena, can you explain how you got your answer?
A group of four students is presented with the following scenario: Two students are playing a game with two standard dice. The dice are rolled and the sum of the two upper faces is noted. If the sum is an even number, Player 1 scores a point. If the sum is odd, Player 2 scores a point. Is this an example of a fair game? Why or why not? The students presented the following responses: Student A: Yes, this is a fair game. Altogether there are 18 ways to get an even sum and 18 ways to get an odd sum. Student B: Yes, this is a fair game. There are only two possible outcomes, even and odd, so each player always has one chance in two of winning. Student C: No, this is not a fair game. There are six even numbers (2, 4, 6, 8, 10, 12) but only five odd numbers (3, 5, 7, 9, 11) so even is more likely than odd. Student D: No, this is not a fair game. For the game to be fair each student must have an equal chance to win a point and they do not. Which student's response is correct? a) Student A because the student correctly analyzed the sample space and determined that there are equal opportunities for odd and even sums b) Student B because the student has correctly concluded that in any experiment where there are exactly two outcomes, the outcomes are equally likely c) Student C because the student correctly analyzed the sample space and determined that there are not equal opportunities for odd and even sums d) Student D because the student correctly defined the idea of a fair game and has arrived at the correct conclusion
a) Student A because the student correctly analyzed the sample space and determined that there are equal opportunities for odd and even sums
A teacher has students with special needs and students with high ability in class. The teacher grouped the students by ability level for a lesson on creating pie graphs to represent data. In the lesson, the teacher is prepared to provide step-by-step instructions for the students with special needs about how to construct a pie graph. The teacher has also planned to engage the high-ability students in constructing a survey to gather data, and creating a pie graph to summarize the data. How effectively does this lesson plan address the needs of all students? a) The lesson effectively addresses the needs of all students. The complexity of the tasks for the different groups of students is based on ability. b) The lesson plan does not effectively address the needs of all students. The students with special needs should not be expected to construct pie graphs. c) This lesson does not effectively address the needs of all students. The step-by-step instructions do not support the students with special needs in meeting the objective. d) The lesson plan effectively addresses the needs of all students because all students finish the assignment with the same product.
a) The lesson effectively addresses the needs of all students. The complexity of the tasks for the different groups of students is based on ability.
A student is asked to compute 2 + 3 x 5 and responds that the answer is 25. What can the teacher conclude about the student's algebraic thinking? a) The student does not follow the correct order of operations. b) The student does not understand the correct use of the equal sign c) The student is correct since this calculation is performed from left to right. d) The student's understanding of basic addition or multiplication facts is incorrect
a) The student does not follow the correct order of operations.
A student is asked to add two fractions and writes the following: 1/2 + 1/3 = 2/5 The student is unsure whether this solution is correct. Which action shows strategic competence? a) The student uses fraction strips to model adding 1/2 and 1/3 and notes that it is equivalent to 5/6 not 2/5. b) The student explains that 1 + 1 = 2 and 2 + 3 = 5 are correct, so 2/5 is correct. c) The student asks another student to show what she did to complete the problem. d) The student asks the teacher for help and is told to use a common denominator, which prompts the student to the correct answer.
a) The student uses fraction strips to model adding 1/2 and 1/3 and notes that it is equivalent to 5/6 not 2/5.
Students are learning about the concept of the perimeter of a rectangle. Which resource would help to effectively teach this concept? a) Geometry software to construct at least five rectangles b) A ruler to measure side lengths of at least five rectangles c) A spreadsheet to enter side lengths of at least five rectangles and a formula to compute the perimeter of each d) A calculator to compute the perimeter of at least five rectangles with the side length measurement provided
b) A ruler to measure side lengths of at least five rectangles
A student is given the following problem: 17 + 42 + 13 When the student is asked how she might solve this problem using mental math, she replies, "Since 42 added to 13 is the same as 13 added to 42, I would add 17 and 13 to get 30 then add 30 to 42 to get 72." What algebraic thinking does this student response demonstrate? a) Correct relational thinking b) Addition is commutative and associative c) The distributive property can be used to simplify computation d) The student produced the correct answer but this process would not generalize
b) Addition is commutative and associative
Which two questions demonstrate effective techniques to elicit mathematical discussion and thinking? Choose 2 answers a) Can you figure out how he got his answer? b) How would you explain your answer? c) How did you figure out the problem? d) How do you state the correct answer to that problem?
b) How would you explain your answer? c) How did you figure out the problem?
A group of students is given the equation 6/8 = 3/4. They are asked to explain the relationship. Which student response demonstrates relational understanding of the concept? a) It makes the pieces smaller. b) It's like 2 quarters equals 5 dimes. c) You reduce and the numbers get smaller. d) You take out the 2 from top and bottom.
b) It's like 2 quarters equals 5 dimes.
Which two activities could be used to make mathematical connections when teaching a thematic unit on the U.S. Thanksgiving holiday in a fifth-grade classroom? Choose 2 answers a) Students create a timeline with the important dates leading up to the first Thanksgiving holiday. b) Students choose a menu for Thanksgiving dinner and determine the cost of the meal using local grocery ads. c) Students take a recipe from their family's Thanksgiving dinner and adjust the ingredients to serve a larger group. d) Students compare crops and planting methods of early European settlers and Native American/First Nation tribes.
b) Students choose a menu for Thanksgiving dinner and determine the cost of the meal using local grocery ads. c) Students take a recipe from their family's Thanksgiving dinner and adjust the ingredients to serve a larger group.
Students in a fourth-grade class work on the following problem: I am thinking of a three-digit number. The number is divisible by 3, 4, and 7. The number is less than 500. The third digit is the sum of the first two digits. What is the number I am thinking of? How should the teacher use a rubric to assess the progress of the students? a) Use the rubric to assess all student work during one class period b) Use a 4, 3, 2, 1 scoring system and equate this to A, B, C, D to assign grades c) Describe the expectations of the rubric to the students before they work the problem d) Use a different method of assessment since this is not a performance-based task
c) Describe the expectations of the rubric to the students before they work the problem
What are two strategies for planning mathematics lessons for all learners? Choose 2 answers a) Choose a specific method that all students will use b) Build in drill exercises to help students learn new ideas quickly c) Provide graphic organizers and tables for students to organize their work d) Include think-pair-share opportunities for students to discuss math concepts e) Design different learning goals and activities for groups of lower-level students
c) Provide graphic organizers and tables for students to organize their work d) Include think-pair-share opportunities for students to discuss math concepts
Student A and Student B are learning how to add multi-digit numbers. Their incorrect attempts to add 542 and 374 are shown here. Student A: 542 + 374 = 8116 Student B: 542 + 374 = 905 Student A and Student B both add 542 and 374. Both students stacked the numbers of the problem vertically to find the sum. Writing is neat and place values are correctly aligned. Student A's response is 8116. Student B's response is 905, and this student carried a 1 to the hundreds place. Which statement explains the confusion that led to the incorrect sums for these students? a) Both students struggle to understand place value. b) Both students struggle with adding single digit numbers accurately. c) Student A struggles to understand place value. Student B struggles to add single digit numbers accurately. d) Student A struggles to add single digit numbers accurately. Student B struggles to understand place value.
c) Student A struggles to understand place value. Student B struggles to add single digit numbers accurately.
The objective of a lesson is for students to learn to measure angles with a protractor. The teacher has grouped the students by ability. All students are given a protractor and a worksheet with pictures of many different angles. Groups of students work together to develop strategies for measuring different angles. The teacher facilitates a class discussion about these strategies after students are finished working. Which two approaches support all students in meeting this objective? Choose 2 answers a) The low-ability group works to decide whether angles measure greater or less than 90 degrees without a protractor. b) Students with special needs work to label angles as acute, right, or obtuse. c) The low-ability group receives extra support to learn to measure angles with a protractor. d) Students with special needs use a protractor to measure fewer angles than the other students.
c) The low-ability group receives extra support to learn to measure angles with a protractor. d) Students with special needs use a protractor to measure fewer angles than the other students.
During an in-class assignment covering the day's lesson on similar triangles, a teacher noticed several students making the following error. Small triangle: Sides: 4 in. and 5 in. Base: 7 in. Large triangle: Sides: 12 in. and 15 in. Base: _____ in. 4/7 = x/12 4(12) = 7x 48/7 = x x = 6.86 in. Two similar acute triangles, one small and one large. The small triangle has the length of all three sides labeled: the left measures 4 inches, the right measures 5 inches, and the base measures 7 inches. The large triangle has two sides labeled: the left measures 12 inches and the right measures 15 inches. The base is left unlabeled. The student work is listed below the triangles in five vertically stacked lines of text. The first line shows 4 over 7 equals x over 12. The second line shows 4 times 12 equals 7x. The third line shows 48 equals 7x. The fourth line shows 48 over 7 equals x. The fifth line shows x equals 6.86 inches. Which part of the lesson should be retaught to help students understand the material? a) Solving ratios b) The properties of triangles c) The properties of similar figures d) Solving one-step linear equations
c) The properties of similar figures
Which scenario demonstrates a context outside of mathematics curriculum where probability could be taught? a) The students solve probability problems on a ten-question quiz. b) The students complete an experiment where they must add fractions using liquid units of measure. c) The students look at the batting average of a baseball player and determine the likelihood of the player getting a hit. d) The students complete a homework assignment where they measure items around the house using nonstandard units of measure.
c) The students look at the batting average of a baseball player and determine the likelihood of the player getting a hit.
Which two statements describe teaching for all students? Choose 2 answers a) The teacher requires all students to complete the same task to be fair and equitable b) The teacher tracks students ability level to provide lower-level and remedial tasks c) The teacher looks for ways to make tasks more relevant to students with varied backgrounds d) The teacher scaffolds tasks to provide access to higher-level thinking for students
c) The teacher looks for ways to make tasks more relevant to students with varied backgrounds d) The teacher scaffolds tasks to provide access to higher-level thinking for students
Students are creating bar graphs from a survey about pet care. How can the teacher incorporate observational assessment into this lesson? a) Ask students to complete an exit slip explaining how they would use bar graphs at the end of class b) Ask each student to create a bar graph using data provided and collect these at the end of the class period and review them c) Use a list of specific content objectives to take notes about student understanding while circulating through the class and then use the data to modify the lesson d) Have a short discussion with the students, at the end of class, about what they know about creating bar graphs and write down highlights of the discussion
c) Use a list of specific content objectives to take notes about student understanding while circulating through the class and then use the data to modify the lesson
A teacher has designed a statistics lesson that requires students to visually present their analysis of the data. How can students use technology or tools to enhance their presentations? a) Use a spinner to model the data b) Use an online forum to discuss the data c) Use a spreadsheet to create a graph of the data d) Use a software application to develop a concept map of the data
c) Use a spreadsheet to create a graph of the data
Which activity could be used to make a mathematical connection within a mathematics curriculum when teaching a unit on multiplying decimals? a) Use manipulatives to demonstrate decimal multiplication b) Create several application problems involving the multiplication of decimals c) Have students research and journal about application of decimal multiplication d) Demonstrate how multiplying fractions is related to multiplying decimals
d) Demonstrate how multiplying fractions is related to multiplying decimals
A teacher has assigned this contextual (story) problem to her class. The Cooper family is having a holiday party for their 3 children. Susan, 10 years old, Noah, 7 years old, and Conner, 5 years old, will each be allowed to have as many guests as their age. If Mrs. Cooper wants to make sure there are 2 cupcakes for each child at the party, how many cupcakes must she bake? If each box of cupcake mix makes 24 cupcakes, how many boxes must she buy? The teacher makes this statement: "Use any representation you wish to understand the problem. "How does this statement make mathematics accessible to all learners? a) It encourages the students to look for key words in the problem. b) It encourages the students to solve the problem by modeling with cubes. c) It encourages the students to choose the correct algorithms to solve the problem. d) It encourages the students to approach the problem from individual perspectives.
d) It encourages the students to approach the problem from individual perspectives.
What is an important characteristic of the process of teaching and learning mathematics? a) Symbolism is the most powerful way to communicate mathematical ideas. b) The concept of proof should be first taught in high school geometry courses. c) The learning of mathematics should be connected to science, but making connections to art and social studies is not necessary. d) Students of all ages should frequently be asked to provide rationale for their answers.
d) Students of all ages should frequently be asked to provide rationale for their answers.
A teacher writes a fifth-grade lesson plan in which students will use a pan balance to demonstrate equalities in equations. The students will use counters and the pan balance to make the equations balance for ten open-sentence equations (15 + 34 = n + 21). The following standard was included within the plan: NCTM (National Council of Teachers of Mathematics): Principles & Standards for School Mathematics: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. How would an administrator rate the learning activity for its overall quality and alignment with the standard? a) The activity was ineffective in demonstrating the concept, but the standard aligned with the lesson. b) The activity was effective in demonstrating the concept of equality in equations, and the standard aligned with the lesson. c) The activity was ineffective in demonstrating the concept of equality in equations, and the standard did not align. d) The activity was effective in demonstrating the concept of equality in equations, but the standard did not align with the lesson.
d) The activity was effective in demonstrating the concept of equality in equations, but the standard did not align with the lesson.