FTCE Math Lesson with questions Competency 01. 02. & 04

Multiple Choice

Which of the following is NOT included in the FTCE Mathematics Subtest study guide as described in the introduction?

• Key concepts

• Vocabulary

• Practice teaching sessions

• Study tips

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Which property is used in the following?

7(8 + 2) = 7 _^x 8 + 7 _^x 2

• Associative Property
• Commutative Property
• Distributive Property
• None of the above

Multiple Choice

How can we practice subitizing?

• Using dice, flashcards, or counting games.

• By counting numbers aloud in sequence.

• Through solving complex mathematical equations.

• By memorizing multiplication tables.

Multiple Choice

Which of the following competencies involves solving linear equations and identifying patterns?

• Competency 01

• Competency 02

• Competency 03

• Competency 04

Multiple Choice

Which of these is NOT another word for iteration

• Repeat

• Loop

• Repitition

• Circulate

Multiple Choice

Each number in Set O goes with one number in Set P. What is the pattern?

• Subtract 1

• Add 1

• Subtract 3

• Add 3

Multiple Choice

Is this pattern growing or repeating?

8, 10, 12, 14, 16, 18, 20

• growing
• repeating

Multiple Choice

What is the 11th term going to be?

• circle

• heart

• A

• B

Multiple Choice

Given the following tile pattern, how many tiles would be in the 5th shape?

• b = 8
• b = 11
• b = 7
• b = 9

Multiple Choice

Is the pattern below a growing pattern or a repeating pattern?

• Repeating because it is an A B C pattern.

• Repeating because it uses the same shapes over and over.

• Growing because there is a change and it does not repeat.

• Shrinking because it gets smaller.

Multiple Choice

Are these patterns the same?

• Yes, they are both repeating. The core of the pattern is AB.

• Yes, both patterns are decreasing. The rule is subtracting by 1.

• The patterns are different. Top one is Repeating Core is AB. The bottom one is adding by 1.

• The patterns are different because one is shapes and the other is fruit.

Multiple Choice

How can we practice subitizing?

• Using dice, flashcards, or counting games.

• By counting numbers aloud in sequence.

• Through solving complex mathematical equations.

• By memorizing multiplication tables.

Multiple Choice

What is an example of subitizing?

• Seeing 3 apples on a table and knowing there are 3 without counting.

• Counting the number of stars in the sky one by one.

• Estimating the number of people in a crowded room.

• Recognizing a friend's face in a group of strangers.

Multiple Choice

Why is subitizing important?

• It helps develop number sense and quick recognition of quantities.

• It is a method for teaching complex mathematical concepts.

• It focuses on memorizing numbers rather than understanding them.

• It is primarily used for teaching reading skills.

Multiple Choice

What is subitizing?

• The ability to instantly recognize the number of objects in a small group without counting.

• A method of counting large groups of objects quickly.

• A technique used in mathematics to estimate values.

• The process of grouping objects based on their characteristics.

Multiple Choice

Iteration is best described as ___ a process or operation.

• modifying
• analyzing
• simplifying
• repeating

Multiple Choice

Which of the following statements about tiling is correct?

• Tiling requires gaps between shapes.

• Tiling is used to study tessellations in geometry.

• Tiling only uses circles.

• Tiling is unrelated to geometry.

Multiple Choice

Tiling is used in geometry to study ___.

• tessellations
• units

• r

Multiple Choice

Name the type of assessment utilized by an exit ticket.

• Formative
• Summative
• Traditional 
• Authentic

Multiple Choice

What type of assessment is a 3D model?

• formative
• summative
• traditional
• authentic

Multiple Choice

Name the type of assessment utilized by a unit test.

• Formative
• Summative

Multiple Choice

Which of the following best describes iteration in mathematics?

• Repeating a process or operation

• Covering a plane with shapes

• Instantly recognizing the number of objects

• Evaluating at the end of a unit

Multiple Choice

Name the type of assessment utilized by a performance rehearsal.

• Formative
• Summative

Multiple Choice

Name the type of assessment utilized by a final project

• formative
• summative

Multiple Choice

Which point is 7/8?

• Point C
• Point D
• Point E
• Point F

Multiple Choice

Name the type of assessment utilized by the rough draft of a paper.

• formative
• summative 

Multiple Choice

Formal Assessments...

• are spontaneous!

• are final exams, tests, and quizzes on subject matter studied.

• made at the beginning of the school day.

• require you to wear formal attire.

Multiple Choice

What is not correct about Informal Assessments?

• Notes students facial expressions.

• It's homework

• Listens to student's explanation of a topic/answer

• Occurs during teaching

Multiple Choice

A history teacher has given a test to their students. The test is twenty questions, each two points. Their grade will represent a percentage. Which form of assessment is this?

• Quantitative Assessment

• Qualitative Assessment

Multiple Choice

 Which graph shows  $$-\frac{1}{5}$$  ?

Multiple Choice

____ is gathering quantitative data of the knowledge and skills students have acquired.

• Evaluation

• Method

• Measurement

• Informal Assessment

Multiple Select

Select all types of assessments mentioned in the slide.

• Summative Assessment

• Formative Assessment

• Diagnostic Assessment

• Norm-Referenced Assessment

Multiple Choice

Formative Evaluation

• Measure students’ acquirement of knowledge and skills to make decisions about their teaching techniques

• Using measurements to decide grades and if the student is ready to move onto next level of education

Multiple Choice

Start at -4. Subtract 4.

What is the final position?

• -5

• -6

• -7

• -8

Multiple Choice

In this type of assessment, a teacher and student discuss progress towards goals, evaluate their work, and reflect on their growth and achievements.

• Self-assessment

• Formal assessment

• Portfolio assessment

• Informal assessment

Multiple Choice

Which of the following is NOT a focus of Competency 01 as described in the overview?

• Operations with fractions

• Operations with decimals

• Operations with percentages

• Operations with integers

Multiple Choice

Project Based Learning

• uses measurements to decide grades and if the student is ready to move onto next level of education.

• is a teaching method in which students gain knowledge and skills by working for an extended period of time to investigate and respond to an authentic, engaging, and complex question, problem, or challenge.

• makes judgements or assigning a value to measurements of student learning.

• assesses what the learner already knows and/or the nature of difficulties that the learner might have, which, if undiagnosed, might limit their engagement in new learning.

Multiple Choice

Validity

• is all about accuracy in your measurements.

• determines consistency.

Multiple Select

Which of the following are considered non-integers according to the vocabulary presented?

• 0.5

• -2

• π (pi)

• 3

Multiple Choice

Norm-referenced assessments

• tests and assessments are designed to measure student performance against a fixed set of predetermined criteria or learning standards.

• standardized assessment that uses a well-defined reference group to establish performance expectations.

Multiple Choice

Which of the following operations can be performed on integers, decimals, and fractions as listed in the key concepts?

• Addition

• Subtraction

• Multiplication

• All of the above

Multiplying Fractions by Fractions

Multiplying Fractions with a Model

Multiple Choice

Which model would you use to represent 3/4 as three out of four equal objects?

• Linear model

• Set model

• Area model

• Decimal model

Multiple Choice

An integer is ...

• Any positive number that is NOT a fraction, decimal, or zero

• Any positive number, including zero, that is NOT a fraction or a decimal

• Any number (positive, negative, or zero) that is NOT a fraction or a decimal

• Any number that can be written as a fraction; it can be made by dividing two integers

• A real number that goes on FOREVER and DOES NOT REPEAT; because they go on forever and do not repeat, they cannot be written as fractions

Multiple Choice

Which problem does the model represent?

• $$\frac{1}{5}\cdot\frac{2}{6}$$

• $$\frac{1}{3}\cdot\frac{2}{5}$$

• $$\frac{2}{5}\cdot\frac{1}{5}$$

• $$\frac{2}{5}\cdot\frac{2}{5}$$

Multiple Choice

A Natural number is ...

• Any positive number that is NOT a fraction, decimal, or zero

• Any positive number, including zero, that is NOT a fraction or a decimal

• Any number (positive, negative, or zero) that is NOT a fraction or a decimal

• Any number that can be written as a fraction; it can be made by dividing two integers

• A real number that goes on FOREVER and DOES NOT REPEAT; because they go on forever and do not repeat, they cannot be written as fractions

Multiple Select

Select ALL classifications that apply to this number:

10

• Real Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Choice

Which model would you use to represent 3/4 as 3 out of 4 equal rectangle parts?

• Linear model

• Set model

• Area model

• Decimal model

Multiple Choice

An Irrational number is ...

• Any positive number that is NOT a fraction, decimal, or zero

• Any positive number, including zero, that is NOT a fraction or a decimal

• Any number (positive, negative, or zero) that is NOT a fraction or a decimal

• Any number that can be written as a fraction; it can be made by dividing two integers

• A real number that goes on FOREVER and DOES NOT REPEAT; because they go on forever and do not repeat, they cannot be written as fractions

Multiple Select

Select ALL classifications that apply to this number:

- 89

• Real Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Choice

After reviewing the introduction to the FTCE Mathematics Subtest study guide, do you have any questions or areas where you would like additional clarification?

• I want to know the passing score for the subtest.
• Can you provide a list of recommended textbooks?
• What is the duration of the subtest?
• Yes, I would like clarification on the types of questions that will be on the subtest.

Multiple Choice

A Whole number is ...

• Any positive number that is NOT a fraction, decimal, or zero

• Any positive number, including zero, that is NOT a fraction or a decimal

• Any number (positive, negative, or zero) that is NOT a fraction or a decimal

• Any number that can be written as a fraction; it can be made by dividing two integers

• A real number that goes on FOREVER and DOES NOT REPEAT; because they go on forever and do not repeat, they cannot be written as fractions

Multiple Select

Which of the following describe ^–77?

Select all that apply.

• irrational number

• rational number

• natural number

• whole number

• integer

Multiple Choice

Which model correctly shows the problem $$\frac{2}{6}\cdot\frac{1}{5}$$  ?

Multiple Choice

A Rational number is ...

• Any positive number that is NOT a fraction, decimal, or zero

• Any positive number, including zero, that is NOT a fraction or a decimal

• Any number (positive, negative, or zero) that is NOT a fraction or a decimal

• Any number that can be written as a fraction; it can be made by dividing two integers

• A real number that goes on FOREVER and DOES NOT REPEAT; because they go on forever and do not repeat, they cannot be written as fractions

Multiple Choice

Breaking numbers into place values is a mental math strategy used for ___ .

• solving equations
• memorizing formulas
• estimating results
• addition calculations

Multiple Choice

Which of the following is an example of a Natural number?

• 5.24

• 8

• $$\frac{1}{3}$$

• 0

Multiple Choice

What problem is represented by the model?

• 1/2 * 3/10

• 3/5 * 9/50

• 3/5 * 3/10

• 2/5 * 3/5

Multiple Choice

Which of the following is an example of a Whole number?

• 5.24

• $$\sqrt{8}$$  
  

• $$\frac{1}{3}$$

• 0

Multiple Choice

Use the model to find the product.

• 35/1

• 2/12

• 1/6

• 1/35

Multiple Choice

Which of the following is an example of an Integer?

• -4

• $$-\frac{2}{7}$$  
  

• $$\pi$$

• 6.15

Multiple Choice

Explain how you would use benchmarks to estimate the sum of two fractions, such as 5/6 and 1/5.

• Approximately 0.5
• Approximately 2
• Approximately 1.5
• Approximately 1

Multiple Choice

Which of the following is an example of a Rational number?

• $$\sqrt{11}$$  
  

• $$\pi$$  
  

• 7.06

• $$e$$  

Multiple Choice

Which fraction model shows 2/5 x 2/3?

Multiple Choice

Which of the following is an example of a Irrational number?

• 95.87

• $$\frac{3}{4}$$  
  

• $$\sqrt{12}$$  

• -6

You can make a friendly number.

• 34 + 28 =

• Take 2 away from the 34 and you get 32.

• Add those 2 to the 28 and you get 30.

• Add 32 + 30 = 62

Topic 2, Lesson 2 Mental Math: Estimate Sums and Differences

Multiple Choice

Explain how subitizing can be useful in early mathematics education.

• Subitizing is primarily used for teaching reading skills.
• Subitizing helps in memorizing multiplication tables.
• Subitizing is a method for teaching writing techniques.
• Subitizing is useful in early mathematics education as it enhances number sense and supports mental math.

Multiple Choice

What is a sum?

• The answer to any math problem.

• The answer to an addition problem.

• The answer to a subtraction problem.

Multiple Choice

Label point C on the number line

• $$\frac{5}{6}$$

• $$-\frac{2}{3}$$

• $$-\frac{2}{6}$$

• $$-\frac{1}{2}$$

Multiple Choice

What is a difference?

• The answer to any math problem.

• The answer to an addition problem.

• The answer to a subtraction problem.

The Essential Understanding

of this lesson is:

There is more than one way to estimate a sum or difference. Estimation gives a way to replace numbers with other numbers that are close and easier to compute mentally.

Reminder

Mental math is being able to mental math calculations in your head. But it is okay to use paper and pencil and record your thought process to get to the answer!

One strategy we can use to add and subtract in our head is to use rounding.

We can ESTIMATE the sums and differences of numbers.

Multiple Choice

True or False: You can estimate to any place value.

• True, but you should be

  precise in your choice.

• False, you have to

  estimate to the hundreds place.

Let's estimate the sum of an addition problem. We will round to the hundred place.

33,498 + 28,609

Poll

What is 33,500 + 28,600?

• 62,000

• 62,100

• 62,200

This time we will round to the thousand place.

33,498 + 28,609

Poll

What is 33,000 + 29,000?

• 62,000

• 62,100

• 62,200

This time we will round to the ten thousand place.

33,498 + 28,609

Poll

What is 30,000 + 30,000?

• 62,000

• 62,100

• 62,200

• 60,000

Each answer was a little different.

That answer is closer to the actual number based on what place you round to.

This same thing applies to subtraction.

Notice the differences when we change the place value to we round to.

Open Ended

What do you notice about the sum or difference as you round further away from the ones and tens?

Multiple Choice

Estimate the sum, rounding each number to the one thousand place.

• 5,000 + 2,000 = 7,000

• 5,000 + 2,600 = 7,600

• 5,000 + 3,000 = 8,000

Multiple Select

To the nearest ten thousand, Calvin estimates the difference of a subtraction problem at 220,000. Select all that could have been Calvin’s original problem.

• 232,684 - 14,652

• 238,041 - 19,558

• 271,982 - 64,780

• 298,155 - 75,437

• 242,698 - 18,765

Next Steps:

Go to Schoolwork to Open EdPuzzle.

Don't forget to Mark Done when you finish EdPuzzle.

Then Open Keynote Practice Buddy.

Don't forget to Submit when you finish.

Multiple Choice

When using benchmarks to estimate the sum of 7/8 and 1/4, what is the approximate answer?

• 1

• 1 1/4

• 2

• 1 1/8

Multiple Select

Which of the following are considered non-integers according to the vocabulary presented?

• 0.5

• 2

• π (pi)

• -1

Mental Math for Addition

You can add the tens, add the ones, and then put them together.

• 34 + 28 =

• 30 + 20 = 50

• 4 + 8 = 12

• 50 + 12 = 62