math ec-6 questions
A first-grade class is finishing a unit on counting sets of coins. Which of the following would be an effective use of technology at the end of the unit? A a video call with a guest speaker who tells students about her job at a bank B an online assessment in which students select the set of coins needed to purchase different items C a multimedia presentation about coins used in different countries D a YouTube video with a song that will help students remember the value of different coins
B
A first-grade teacher is planning a lesson on solving problems with an unknown addend, such as 3 + __ = 8. She knows that students have struggled with this concept in previous years and is looking for a way to engage students with technology while still improving their understanding of the concept. Which of the following could she do in order to achieve this? A Make sure to include several practice problems that include unknown addends on an online math program students use. B Use an interactive part-part-whole model that allows students to drag items from the "whole" to the "parts" to find the unknown addend. C Use a video with characters the students enjoy that demonstrates how to solve these types of problems. D Ask another teacher who has had success teaching this concept to record herself explaining it so it can be shown to the class.
B
A third-grade teacher is planning an introductory lesson on perimeter. Which of the following would be the most appropriate to include in the lesson? A a sheet that students can glue in their math journal that includes the formula for perimeter B an activity in which students are given the dimensions of the school garden and asked to work in groups to determine how much fencing they would need to enclose the garden C a YouTube video that uses a song to help students remember how to find perimeter D a class survey to see how many students have heard the term perimeter before
B
Base ten blocks are commonly used by teachers to illustrate the concept of: A adding within ten. B place value. C one-to-one correspondence. D adding two-digit numbers.
B
Crosby has 2/3 of an hour to write an essay. If he can write one paragraph in 1/9 of an hour, how many paragraphs can Crosby write in the given amount of time? A 3 B 6 C 9 D 18
B
Mr. Marks gives his students a pop quiz on graphing on the coordinate plane. Sixty percent of his students fail the quiz. What should he do next? A Move onto the next topic. B Reteach the (x,y) coordinate structure and axes to the whole class. C Have students who passed the quiz tutor those who failed the quiz. D Give the students who have the concept mixed up additional reading and homework.
B
Mrs. Herschend decided not to give a test about ratios and instead had her students do a project to display their knowledge. She has decided that she will do this for every unit going forward. What is the main disadvantage to this approach? A Projects take more class time than giving a test. B Students need to practice test taking skills periodically. C Parents can help with projects and the students knowledge may not be displayed. D Some students are not creative and projects are more stressful than tests.
B
Of the following higher-order thinking questions, which would be the most appropriate in a fourth-grade classroom? A Predict how the data you collected in your project will change over the next decade. Justify your answer. B Identify the mathematical rule that applies to this situation. Explain your reasoning. C Using the information you have collected, create a bar graph to display the data. D In your own words, generalize the mathematical rule that applies to this problem.
C
Students are plotting improper fractions on a number line. Quincy places a fraction between the 5 and the 6 on the line. If the denominator is 3, which of the following could be the numerator? A 15 B 14 C 17 D 20
C
What is 5/18 as a percent? A 51.8% B 0.278% C 27.78% D 5.18%
C
When solving an equation, Allie and Diane chose to take different approaches in their first steps. Which property ensures that they are both correct? Original equation: 5x+3x−2x=4 Allie's approach: (5x+3x)−2x=4 Diane's approach: 5x+(3x−2x)=4 A multiplication property of equality B addition property of equality C associative property of addition D commutative property of addition
C
Which of the following activities would be most effective in helping first-graders understand partitioning 2-dimensional shapes into equal parts? A watching the teacher draw a line on a 2-dimensional shape to divide it into 2 equal parts B placing cubes on top of 2-dimensional shapes to see how many cubes it takes to fill the shape C cutting out different shapes and having students fold them into 2 or 4 equal parts D use a ruler to measure the perimeter of different 2-dimensional shapes
C
A second-grade teacher is planning a lesson on measuring length using standard units. Which of the following would be an effective way to engage students in the lesson while allowing them to practice measurement strategies? A Using an online program that allows students to use an on-screen ruler to measure objects. B A worksheet that includes measurements of toys the students like. C Asking students to predict the length of common household items. D Going outside to measure various parts of the playground in inches, feet, or yards.
D
A third-grade teacher is planning a lesson on representing data using dot plots. She plans to introduce the concept of dot plots, show examples, and create a class dot plot that shows how many siblings the students have. Which of the following would be the best way to incorporate technology into this lesson? A an internet search of dot plots so students can view several examples B an online video that demonstrates how to make a dot plot C a quiz on dot plots that students complete independently on the computer D an online program that allows students to plot their data point on a dot plot
D
Interest is best defined as: A the amount of money someone can spend on a credit card. B the minimum a borrower must pay each month on their credit card bill. C the discount provided by using a credit card. D the cost associated with borrowing from the bank which issues a credit card.
D
Maria solved a word problem and correctly gave 72 as the answer. Which of the following could not have been the question asked? A What is the least common denominator of two numbers? B What was the average temperature, in Fahrenheit, in the city in March? C How many guests were in attendance at the party? D How many months did Alexa achieve perfect attendance last year?
D
Mr. Jones is hosting a career day for his sixth-grade class. Jeremy tells him that his father cannot come present because his job has nothing to do with math because he did not attend college. Mr. Jones asks Jeremy what his dad does for a living. Jeremy says his dad is a carpenter. What should Mr. Jones tell Jeremy? A Carpentry involves a lot of math including accurate measurements, determination of angles, and geometry. B Carpentry involves algebra to determine how much raw material to buy. C Mathematics is used by people throughout their lives, whether or not they attend college. D All of the above.
D
What is the greatest odd factor of 5,824? A 64 B 57 C 13 D 91
D
Which of the following has the least value? A 0.5108 B 0.5018 C 0.518 D 0.0518
D
Which of the following is the best way for elementary students to be introduced to rectangular arrays? A During math games, use an array as part of a question B Giving them sample problems with arrays C Watch an online video over arrays D Using manipulatives such as 10-blocks to create their own arrays
D
Which of the following numbers is neither prime nor composite? A 4 B 3 C 2 D 1
D
Which of the following would be an appropriate time for a classroom teacher to use a formative assessment? A as a closing activity at the end of a class period B when students are involved in a cooperative group project C as the teacher is introducing a new concept D all of the above are good times for a formative assessment
D
In a unit on personal finance, a sixth-grade teacher wants students to be able to identify the difference between fixed and variable costs. Which of the following examples would best highlight this difference? a. having students ask their parents what fixed costs they pay each month b. analyzing the money spent on gas each month of an average American and looking at how much a person drives impacting the price they will pay in gas c. looking at the differences between a tax deduction and a tax credit d. categorizing the expenses of a local restaurant into expenses that depend on the number of customers and expenses that do no not depend on the number of customers
d
Johnny wants to make a graph to display the amount of money the military spent over a period of time. Which graph would best display this data? a.stem and leaf plot b.dot plot c.double bar graph d.line graph
d
Which expression can be used to solve the following word problem? John and Jose want to buy a pizza for dinner and then head to a movie. They will each pay for their movie ticket, which costs $12 each, and they will split the pizza cost of $9. John has $17 and Jose has $20. How much will Jose have left at the end of the evening? a. 20 + 17 - 9 - 12 b. 9/2 + 12 c. 17 - (9/2 + 12) d. 20 - (9/2 + 12)
d
Which number below has an exponential form of 7 × 109? A 7,000,000 B 70,000,000 C 700,000,000 D 7,000,000,000
d
Which situation could best be represented by the equation: 12�=5412x=54? a. Marty earns $12 for typing a paper. If her rate is $54 per hour, what is x, the number of hours it actually took to type the paper? b. Marty collected 12 dozen eggs every day for 54 days. What is x, the total number of dozens of eggs she collected? c. Marty had 54 minutes left on his cell phone plan. If he uses 12 minutes, what is x, the number of minutes remaining on his cell phone plan? d. Marty made car payments on her car for 54 months until it was paid off. What is x, the number of years it took Marty to pay off her car?
d
Michelle is assigned homework to flip a coin 10 times, then 100 times, then 1000 times. She decides to use her computer to generate a 1 for heads or a 2 for tails. She has the following results: The students are then asked to calculate the percentage of flips that are heads versus tails. What topic is the teacher wanting students to explore? a.theoretical probability b.decimal to percent conversions c.fraction to percent conversions d.empirical probability
empirical probability
inductive reasoning
generalizing knowledge from one area to another. If a random sample of a population shows a correlation in improved health with a new drug, it can be induced that the drugs will be helpful for others in the population.
conjectures
guesses without proof while doing mathematics
division property of equality
if a = b and c is not equal to 0, then a/c = b/c If the quantities on each side of an equal sign are both divided by the same amount, the resulting statement will still be equal.
in ________ reasoning, broad statements are made from some data to create conjuctures. in ________ reasoning, true statements are used to make a proper conclusion and evaluate a conjectures validity
inductive; deductive
stop and ask yourself, does the answer _______
make sense
Jesse surveys 20 people about her new ice cream flavor that she plans to start selling in her ice cream shop. She asks her customers to rate a sample of the new ice cream on a scale of 1-10, 1 meaning they dislike the ice cream and 10 meaning they really like the new ice cream flavor. The data below represents her results 10, 10, 10, 10, 10, 10, 10, 10, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 Jesse concludes she will not sell the new flavor in her shop because the average of her responses is 5, meaning there was not a strong preference for this flavor. Which measure of central tendency would provide a better indicator for her to base her decision? a. Mode b. range c. median d. mean
a
John made a circular garden in his backyard. The garden has a diameter of 20 feet. He used ⅓ of the garden for tomatoes, his favorite vegetable. He enclosed the entire garden with a picket fence that was 12 inches high. Which of the following questions could NOT be answered with the information provided? a.What is the volume of the dirt in the garden? b.What is the area of John's garden? c.How many feet of fence does John need? d.What is the area of the tomato patch?
a
Simplify the expression: 30−2×50+7030−2×50+70 a. 0 b. -70 c. 1470 d. -210
a
The west wall of a square room has a length of 13 feet. What is the perimeter of the room? a. 52 feet b. 48 feet c. 169 feet d. There is not enough information
a
Tom wants to mentally calculate a 20% tip on his bill of $40. Which of the following is best for Tom to use in the mental calculation of the tip? a.40 × .1 × 2 b.40 × .02 c.40 × (200/1000) d.40 × (20/100)
a
When teaching geometric shapes, Mr. Gaines challenges his students to prove a statement right or wrong. He writes on the board, "All rectangles are parallelograms and all squares are rectangles; therefore, all squares are parallelograms". What type of thinking is trying to promote? a. deductive reasoning b. inductive reasoning c. empirical reasoning d. conjectured reasoning
a
Tosha has 8 coins in her pocket. She has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. What is the largest amount of money she could possibly have? a. $1.21 b. $1.11 c. $1.23 d. $1.07
b
Who is credited with creating much of what we consider geometry? A the Indians B the Greeks C the Babylonians D the Americans
b
Which of the following numbers is the product of one even number and two odd numbers, assuming the factors are greater than 1? A 12 B 18 C 20 D 28
b use a factor tree
an operation can be applied to an equation, as long as the same operation is applied on ______ _______ of the equal signs
both sides
A journalist in a town with a population of 15,200 takes a random sample of 200 people and finds that 60 of them read the local newspaper. Based on this sample, which of the following is the best estimate for the number of people in the town that read the local newspaper? a. 5 b. 45 c. 4500 d. 450
c
The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500? a.$500 + $2b = $0.75b b.$500 = $2b + $0.75b c.$500 = $2b - $0.75b d.$500 - $0.75b = $2b
c
Which number could be added to the data set below so that the range stays the same? 23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26 A 0 B 2 C 55 D 103
c
Which of the following is not equivalent to 62,000? A 62 thousands B 6200 tens c 6200 hundreds d 620 hundreds
c
Who is credited with creating much of what we consider geometry? a. the Indians b. the Americans c. the Greeks d. the babylonians
c
Rick pulled a card at random from a normal deck, noted it, replaced it, shuffled, and drew again. His draws were as follows: 10, J, 10, K, 1, 2, 6, 10, 11, 4 What is the probability that he will draw a 10 on the next draw? a. 3/8 b. 3/10 c. 1/13 d. 1/4
c If the cards are replaced and shuffled, each draw is a simple independent event. You should ignore the extra information of what he drew so far. Since there are 4 10's in a standard deck of 52 cards, the probability of a 10 is 4/52 = 1/13.
A mathematics teacher determines that the median score for the most recent test was 80 percent. Which of the following is the most accurate interpretation of the result? a.The average score on the test is 80 percent. b.The most common score on the test is 80 percent. c.Half the students scored an 80 percent or below. d.The highest score on the test was 80 percent.
c.
Students in Mr. Jaffrey's class were discussing in pairs if the following mapping diagram represents a function: 2-4 5-4 8-4 (all go to 4) As Mr. Jaffrey was circulating, he overheard Reena tell her partner that the relation is not a function because every input gives the same output. Of the following, which is the best response for Mr. Jaffrey to give Reena? a. Reena, you are correct. The relation is not a function the same output corresponds with multiple inputs. b. Reena, you are correct that the relation is not a function, but your reasoning is not accurate. Instead, it is not a function because each input corresponds with only one output. c. Reena, you are incorrect. Even though each input gives the same output, there is only one output for every input, so the relation still represents a function. d. Reena, you are incorrect. The relation is a function because all of the output values are the same.
c.
During a lesson on using models in mathematics, a teacher asks the students to figure out how many hours they spend on homework for all their classes each year. In asking this question, the teacher has asked the class to: a. demonstrate the use of symbols to represent mathematical quantities. b. demonstrate their proficiency with the use of proofs. c. demonstrate their ability to use statistics with data. d. demonstrate an understanding of the estimation process.
d
In a first-grade class, the students have been working with manipulative materials and pictures as they investigate the concept of addition. Through both formative and summative assessments, the teacher has determined that the students are ready to move to more abstract (pencil and paper) ways to represent addition. How should she begin this process? A. Model one of the problems, 7 + 2 for example, for the children by writing: 7 + 2 = 9. Then have the students repeat the process with a different problem. B. Relate the symbolic representation of addition facts to models the children have created, modeled, or drawn in their math lessons. C. Give the students a page of one digit addition problems with sums of 10 or less and having them draw a picture to match the sum. D. Have the children model pictorial representations of problems like 7 + 2 = 9 that include the numbers that represent each step.
d
associative property of addition
(a+b)+c=a+(b+c) you can move the parentheses
Jessie draws a marble from the bag shown (10 marbles, 3 are red)and then, without replacing the first marble, he draws a second one. Which expression shows the probability that he drew a red marble both times? a. 3/10 • 3/10 b. 3/10 • 2/9 c. 3/10 • 3/9 d. 3/10 • 2/10
3/10 x 2/9 This is an example of dependent events. P(red) = 3/10 for the first draw. However, the first marble is not returned to the bag, changing our sample to 9 marbles. If the first marble drawn was red, that leaves only 2 red marbles, so on the second draw, P(red) = 2/9. The probability of both events happening is the product: 3/10 • 2/9.
f 2.2 lb = 1 kg, and Mary weighs 120 lbs, how much does she weigh in kg? a.120 kg b. 264 kg c. 55kg d. 60 kg
55kg 1kg/2.2lb=xkg/120lb
A first-grade class has been working on place value for several days. The teacher notices that some students are still struggling with the basic concept, some students are improving but still need additional practice, and some students have caught on quickly and are becoming bored. She plans to work with students in small groups while the rest of the class works in stations or independent work. What would be the most appropriate way to group students in this scenario? A homogeneously B by seating arrangement C heterogeneously D randomly
A
A first-grade teacher has created three different ramps by stacking large blocks and laying pieces of cardboard from the tops of the block towers to the floor. One ramp is built with two large blocks, one with three, and one with four. After students have had a chance to roll a ball down each of the ramps, the teacher decides to ask students a question. Which of the following questions is most appropriate to ask at this point in the experiment? A "What have you noticed about how the ball rolls differently with the different ramps?" B "What can you conclude from this experiment?" C "Which of the ramps is the steepest?" D "Why does the ball roll farther with the ramp built from four blocks?"
A
A second-grade teacher is planning an introductory lesson on ordering numbers on open number lines and wants to incorporate technology into the lesson. Which of the following would be the most effective use of technology in this scenario? A an interactive number line on which students can drag and drop numbers to the correct place B an online quiz in which students identify the correct number that's missing from a number line C a video showing when number lines are used in real-world situations D an online video that explains how to place numbers on a number line
A
A sixth-grade teacher is beginning a unit on probability. She utilizes the following steps in planning her unit: 1.Determine the necessary prerequisite skills. 2.Begin planning probability activities that involve the collection of data. 3.Determine what the students already know by using a KWL chart. 4.Plan the final assessment for the unit. What is the best order for the teacher to organize these steps? A IV, I, III, II B I, III, II, IV C I, III, IV, II D I, II, III, IV
A
A student asks a teacher when calculating percentages of numbers will be useful in real life. Which of the following examples would be the most appropriate response for the student? A. a parent going shopping at a store sale B. a pharmacist measuring the correct amount of medication C. a builder cutting materials for a house D. a architect designing a building
A
According to the TEKS, which of the following is an appropriate skill for a second-grade student to master during a unit on numbers and operations? A Students will be able to place a given whole number in the correct position on an open number line. B Students will be able to create a Venn diagram of the characteristics of their classmates. C Students will be able to identify three-dimensional solids, such as a cylinder or cone. D Students will be able to compare and order decimals to the hundredths.
A
Mr. James plans to assess his students' knowledge during a unit on linear functions and would like feedback from the students on how well they feel they are learning the concepts. Which of the following assessment would be the most appropriate for Mr. James to use during the unit? A Daily open-ended formative assessment in which the students complete a problem, with justification and any questions they still have about the material from that day. B An observation checklist that Mr. James uses to check off student names when they get a problem right. C Weekly Friday quizzes that cover the objectives from that week. D An end of unit project that incorporates all of the objectives learned in the unit into one task.
A
Mrs. Doloff's third-grade class has learned about ordering people according to age when given a word problem such as "John is older than Mei and Mei is older than JD. Who is oldest?" What is the next concept for Mrs. Doloff to teach about ordering? A adding numbers to the problem to solve for exact age B adding algebraic terms so that each person is represented by a letter such as person A, B, C C teaching them to order based on height with numbers D teaching them to order based on height without numbers
A
Ms. Hobbs is planning to introduce long division to her students for the first time. Which of the following would be the best first instructional step for this topic? A quiz students on their understanding of basic division before proceeding B work a complex example on the board for the students to see C have students memorize the steps for long division D present long division through an abstract form or concept
A
What is the greatest odd factor of 2,496? A 39 B 13 C 27 D 3
A
Which of the following is NOT considered a benefit of cash? A security B acceptability C accessibility D ease of use
A
Which of the following statements best describes a formative assessment? A Formative assessments measure what students know along the way. B Formative assessments are given at the end of the grading period. C Formative assessments measure what students know at the end of a unit. D Formative assessments are given at the end of each year.
A
Use the student work shown below to answer the question: Step 1: 3x+2=16−4x Step 2: 7x+2=16 Step 3:7x=14 Step 4: x=2 Which property should the student use to justify step 3? A addition property of equality B transitive property C multiplication property of equality D associative property of addition
A To go from step 2 to step 3, the addition property of equality was used when -2 was added to each side and the inequality remained true.
Which of the manipulative materials below would be most suitable for teaching decimal notation to the hundredths place? Select all answers that apply. a.base ten blocks b.tangrams c.geoboards d.decimal squares e.pattern blocks
AD
A fifth-grade teacher is preparing to launch a unit focused on multiplying and dividing fractions. Which of the following concepts should he include on the pre-unit diagnostic test? A FOIL B finding simplest form C PEMDAS D decimal place value
B
formal reasoning have a __________ answer informal reasoning has a more __________ answer
single;open-ended
stimulating higher order thinking tips
-ask open ended question -scaffold learning with clarigying questions -allow wait time -allow students to talk w partner -use incorrect answers as a learning opportunity -spend time establishing expectations for class discussion
teachers can help students develop mathematical reasoning skills through a variety strategies:
-explicitly teach multiple strategies -asking students to explain how they arrived at their answer -demonstrate another way to do the problem -remind students to ask themselves if their answer "makes sense" -ensure students have a strong foundation
solution strategies
-guess and check -make an organized list -solve a simpler problem -work backwards -use a formula -draw a picture or use a model
Students are asked to solve the word problem below. The school carnival is coming up and Jenny and Sarah plan to sell cupcakes. Since the school carnival is a fundraiser, Jenny and Sarah's parents make a donation to their cupcake booth to get them started. Jenny starts with a $5 donation and sells her cupcakes for $3 each. Sarah starts with a $10 donation and sells her cupcakes for $2 each. How many cupcakes do Jenny and Sarah have to sell for their profits to be equal? One student's response is "Zero, because if Jenny sells her cupcakes for more money, then she will always have more profit." Which of the following activities could help the student realize his misconception? A using mental math B graphing the scenarios C baking cupcakes D the student does not have any misconceptions, the student's answer is correct
B
Colin is a child learning about animals. He notices that dogs have four legs and a tail. When he sees a cat he incorrectly calls it a dog. What type of reasoning is Colin using? A informal reasoning B inductive reasoning C deductive reasoning D formal reasoning
B. inductive reasoning is generalizing knowledge from one area to another to make predictions
Jayce is a first-grade student struggling with comparing two-digit numbers. Which two of the following manipulatives could his teacher use to provide support for Jayce? Select all answers that apply. A counters B Unifix cubes C base ten blocks D Cuisenaire rods
BC
Ms. Colon, a new fifth-grade teacher, is planning her math lessons for the grading cycle. She thinks of all of the topics she needs to teach and makes discrete daily lessons. Each unit has an opening pre-test. Each lesson has instruction, guided practice, and independent practice. Which of the following are methods she should incorporate into her lesson planning? Select all answers that apply. a. Instead of pre-testing students before each unit, begin new material as soon as possible b. Plan time each day for students to explain concepts they have learned to their peers. c. Plan each lesson with a closure activity. d. Instead of making single lesson plans, first create a thematic unit around which to frame her lessons.
BCD
Which of the manipulative materials below would be most suitable for teaching decimal notation to the hundredths place? Select all answers that apply. A tangrams B decimal squares C geoboards D base ten blocks E pattern blocks
BD
A student asks the teacher who invented the number system we use today. Which of the following answers would be most appropriate? A The current number system has evolved over a period of thousands of years and each culture contributed to its development. B The current number system was developed by the Greek and Roman empires. C The base-ten number system was developed by the Hindu-Arabic civilizations. D The base-ten number system was invented by Isaac Newton in the late 17th century.
C
Hy is interviewing new candidates for a position at his company. If he schedules 1331 of an hour for each interview, how long will it take him to interview 66 applicants? A 1/18 hour B 1/2 hour C 2 hours D 18 hours
C
Miss Kelly has been teaching fractions and believes her students understand composing and decomposing fractions through the activities they have done. What activity would be best to informally assess their knowledge before moving on to the next lesson? A Include fraction composition and decomposition in the homework tonight B Lead a discussion on fractions in the real world C Provide a warm-up question that asks them to write one way to decompose 3/4 D Give a short pop quiz with fraction composition and decomposition
C
Mr. Stiles is introducing measurement to his third-grade class. He has rulers, stopwatches, scales, and graduated cylinders available for them to use. Based on previous lessons, he knows that most students do not know how to use these tools correctly. What is the best introductory lesson for this unit? A stations that go with a worksheet packet B a demonstration on how to use each tool C providing students time to explore the items and then creating a K-W-L chart D a pre-quiz that requires the use of each of the tools
C
Mrs. Luna tried flipping her classroom to teach common denominators, having students watch a lecture at home and then doing the homework practice during class. Many students did not watch the entire video because they thought they had the concept down after the first example. If she tries this again, how should she change her approach? A Have students create the video. B Give prizes for those who watch the entire video. C Provide a notes outline that needs to be filled in as they watch the video. D Keep students inside during recess if they did not watch the entire video so they can catch up.
C
Ms. Daniels is a second-grade teacher who notices that several of her students are struggling to determine the value of an unknown addend in an equation. She plans to reteach this concept in small groups to the students who are struggling. Which of the following manipulatives would enhance Ms. Daniels' small group lessons on this topic? A algebra tiles B fraction tiles C Cuisenaire rods D number lines
C
Ms. Ma is teaching her students about subtraction. On her exit ticket she asks "What is the difference between 21 and 14?" Several students answer 35. Another question she asks is "25-6 =___" to which every student answers 19. What should Ms. Ma teach tomorrow? A a lesson on division B a lesson on the differences between addition and subtraction C a lesson on math vocabulary focusing on keywords in word problems D a lesson on subtraction
C
Multiplication Property of Equality
If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal. If a=b, then ac=bc
Addition Property of Equality
If the quantities on each side of an equal sign have the same amount added to them, the resulting statement will still be equal. if a=b then a+c=b+c
subtraction property of equality
If the quantities on each side of an equal sign have the same amount subtracted from them, the resulting statement will still be equal. If a=b, then a-c=b-c
A teacher engages her class in a discussion of the coordinate plane. The students are asked to identify the quadrants, the coordinate axes, and the mathematical notation for various points in the plane. Students are asked to develop a way to quickly identify the quadrant in which various points lie. Which of the following objectives is the teacher most likely trying to address with this lesson? a.developing precise mathematical language when expressing mathematical ideas b.demonstrating how to model and solve real-world problems using mathematics c.augmenting an understanding of estimation and its appropriate uses d.encouraging student use of mathematics manipulatives and technological tools
a.
Mr. Fischer, a bilingual teacher, teaches a mathematics class composed of native English speakers and English language learners (ELLs). He has introduced a new topic with new vocabulary words in which he presented the vocabulary words with several examples. Which of the following strategies should Mr. Fischer use next to check each student's understanding of the vocabulary words? a. having students write a definition for each term in their own words in their native language b. having students copy down the definition for each word that Mr. Fischer wrote on the board in English c. placing students in groups so each student can explain the vocabulary terms to their peers in English d. having students look up the definition online to see if it matches what Mr. Fischer told them
a.
informal reasoning is used to ____
answer questions and solve problems that are complex and open ended -use every day knowledge to synthesize information and reach a conclusion
formal reasoning is used to
answer questions and solve problems that have a single solution -use roles of logic and algorithims
A second-grade teacher is introducing the idea of measuring using inches and centimeters. Which would be the most effective beginning activity? A giving the students rulers to measure one irregular object in both units B having the students find what objects are roughly an inch long in the classroom C asking each student to measure their hand in inches for homework D demonstrating conversion using linking cubes.
b
A third-grade teacher is introducing the idea of adding areas of smaller rectangles to make one larger rectangle. Which would be the most effective beginning activity? a. identifying which shapes are rectangles b. having the students explore rectangles that all have the same width c. demonstrating how to put two rectangles next to each other d. leading a discussion about squares as special rectangles
b
Bill went to the store to purchase new clothes for the upcoming school year. Bill purchased 8 shirts, 4 pairs of shorts, and 2 pairs of pants. If a single outfit consists of one shirt and either one pair of shorts or one pair of pants, how many outfits can Bill create with the clothes he purchased? a. 16 b. 48 c. 32 d. 42
b
formal reasoning
the use of logic and algorithms to reach conclusions answer questions and solve problems that have a single solution
informal reasoning
used to answer questions and solve problems that are complex and open-ended (without a definitive solution) Compare pros and cons
deductive reasoning
using two or more known premises to draw a conclusion All cats say meow. (premise #1) Jackie is a cat. (premise #2) Therefore we can deduce that Jackie says meow. (conclusion)
