Math Final 4100

Choose a fraction number that represent the area with the red rectangle.

1/16

Choose fractions to order the fractions from the least to the greatest. 1/3 6/10 5/8

1/3 6/10 5/8

What is 629 rounded to the nearest hundred?

600

Product

A multiple of each factor (multiplicand and multiplier)

Finding a pattern

An efficient way to solve some problems is to record data in a table and then look for a pattern

Which property is this following diagram showing? (3x2)x4=24 3x(2x4) =24

Associative

Process Problems

At an air show, 8 sky divers were released from a plane. Each skydiver was connected to each of the other skydivers

What do we call our system? This is the number of objects use in the grouping process. Our system is a _________system. Wherever we have 10 or more objects, they may be regrouped to make one group of the next larger place value. There is n one numeral for ten, rather, the number 10 is expressed as 1 ten and 0 ones, or 10. There are ten digits in the ________________system. 0 through 9.

Base Ten

The fact that two objects that are the same may have different values is not difficult for children to understand.

False

The idea of equivalent fractions can be introduced early to children. So mastery of the concept should be expected in early grades.

False

Which statement explains tasks and material appropriate for problem solving?

Be motivating and culturally relevant Sometimes contain missing or contradicting information Involve children in activities that promote communication and math thinking Engage children in activities that use diverse problem-solving strategies

Which property is this flash card going to help kids learn? 9x4 4x9

Commutative

Megan has 3 stickers. Randy has 8 stickers. How many more stickers does Randy have than Megan?

Compare-Difference Unknown

The [ ] strategy involves increasing one addend while decreasing the other by the same amount.

Compensation

The number line is not a difficult model for children to understand and should be the first model to represent an operation.

False

Mark all activities proper to consolidate basic facts.

Computer software, puzzles, games

To examine whether or not a child has this ability, have the child count two sets of the same objects such as Unifix cubes.

Conservation

This strategy involves beginning with one addend and counting on the number of the second addend. For example, to solve the problem 6+3, ah child could start with 6 and count forward three times, saying seven, eight, nine.

Counting On

When assessing fraction number sense, teachers should ask students to model fractions using concrete representations only.

False

Mark all reasons that children should explore different algorithms.

Different algorithms may help children develop more flexible mathematical thinking and number sense. Awareness of different algorithms demonstrates the fact that algorithms are inventions and can change Different algorithms provide variety in the math class. Different algorithms may serve reinforcement, enrichment, and remedial objectives

[ ] refers to the process in which children use concrete materials to exactly represent the problem as it is written.

Direct Modeling

One of the most useful strategies for computing a multiplication exercise mentally is to employ the [ ]. For example, 5×76 can be computed as (5×70) + (5×6).

Distributive Property

The belief that mathematics needs to be meaningful and the idea that children construct their own math knowledge does rule out the need for practice.

False

The estimation is not necessarily a legitimate mathematical tool

False

Cramer and Whitney (2010) describe four categories of fractions to compare. Which category is the easiest one for students to compare?

Fractions with the same denominator

Students begin to learn fractions when they learn about [ Select ] in [ Select graders.

Geometry 1st

Chuck had 3 peanuts. Clara gave him some more peanuts. Now Chuck has 8 peanuts. How many peanuts did Clara give him?

Join-Change Unknown

Select all items that belong to number relationships

More than fewer than part part whole one greater than one less than order relations

in the video is multiplication and the kid in the video is using derived facts .

Multiplication Derived Facts

A digit

Numbers 0-9

Writing an open sentence

Some problems can be solved by writing an open sentence and then solving it.

Act it out

Sometimes children may want to model the situation in the problem

Select statements that are not idea as a teachers role in problem solving instruction

Teach children how to prevent them from making mistakes and expect specific responses from students.

Divisor

The number in each group

Multiplicand

The number in each group

Multiplier

The number of groups

Remainder

The number of objects that cannot be shared equally

You might ask a child who has displayed five fingers whether he or she could show the number in the same way. This is called

Translation

In learning problems like "a gardner has 60 feet of fence to keep animals out of the garden. What is the largest area of garden that this fence will enclose? may be effective to develop constructing a table or chart.

True

There was an addition problem: Ray has 6 goldfish. But he wants 13. How many more does he need to buy? Corey solved this problem. He said, "Six plus six is twelve, and one plus is seven is thirteen." We can say that he was using derived facts.

True

To help students make better sense of representing numbers, many researchers and teachers have recommended teaching children by beginning from concrete models.

True

US students exhibit this misconception much more often than students in other countries.......

True

Cardinal Numbers

Used to designate the quantity of a set

A numeral

a symbol used to represent a number

There are two different ways or algorithms the sharing and place-value language could be translated into a paper-and-pencil recording process. The name of the following algorithm is called the [ ] algorithm.

ladder

A number

mathematical object used to count, measure and label

__________________________is simply saying the numbers in order, usually starting with 1,2,3,4,5

rote counting

Write two sentences that answer each question. Which fraction is more? 4/5 and 6/7 How do you know?

4/5 is smaller than 6/7 because the LCD is 35 and when you rewrite the fraction with the LCD, the fractions become 28/35 and 30/35 and 28 is smaller than 30. If you look at the denominators 5 is less than 7. The numerators are 4 and 6 where 4 is less than 6 so 4/5 is smaller than 6/7. Therefore 4/5 is less than 6/7.

Kindergarten students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the ______________________________of small objects.

Cardinality

Mark has 6 mice. Joy has 11 mice. Joy has how many more mice than Mark? Carl counts out a set of 6 cubes and another set of 11. He puts the set of 6 cubes in a row. He then makes a row of the 11 cubes next to the row of 6 cubes so that 6 of the cubes are aligned with the 6 cubes in the initial row. He then counts the 5 cubes that are not matched with a cube in the initial row. Carl responds, "She has 5 more."

Compare-Difference Unknown Direct Modeling

The type of the problem in the video is Join-Change Unknown and the kid in the video is using Counting strategy .

Join-Change Unknown Counting Strategy

The type of the problem in the video is Join-Change Unknown and the kid in the video is using direct modeling

Join-Change Unknown Direct Modeling

Ellen had 3 tomatoes. She picked 5 more tomatoes. How many tomatoes does Ellen have now?

Join-Result Unknown

Deborah had some books. She went to the library and got 3 more books. Now she has 8 books altogether. How many books does she have to start with?

Join-Start Unknown

Ordinal numbers

Means order or to denote the order of an object

Problem 1. Megan has 15 cookies. She puts 3 cookies in each bag. How many bags can she fill? Problem 2. Megan has 5 bags of cookies. There are 3 cookies in each bag. How many cookies does Megan have all together? Problem 3. Megan has 15 cookies. She puts the cookies into 5 bags with the same number of cookies in each bag. How many cookies are in each bag?

Measurement Division Multiplication Partitive Division

>> Adam has $0.21. Gum drops costs $0.3. How many gum drops can Adam buy with the money he has? >> Seven. >> Okay. Show me how you got that. >> Counted by threes. >> Could you count by three, so we could hear it? >> 3, 6, 9, 12, 15, 18, 21. >> Good job.

Measurement Division Counting Strategy

What is 7, 596 rounded to the nearest hundred?

7,600

Many beginning teachers believe that children will automatically memorize basic facts if they just get enough practice. One very effective strategy to help children learn basic facts is the three-step approach.

Answer 1:Understanding the meaning of the operations Answer 2:Using thinking strategies to retrieve facts. Answer 3:Using consolidating activities for drill and practice.

A restaurant puts 4 slices of cheese on each sandwich. How many sandwiches can they make with 24 pieces of cheese? Susan counts, "Hmm, 4, 8, 12, 16, 20, 24." With each count Susan extends one finger. When she is done counting, she looks at the six extended fingers and says, "6. They can make 6 sandwiches." Problem type is measurement division and strategy the kid is using in the video is counting strategy .

measurement division counting strategy

Mark all that belong to proportional base ten materials

meter, decimeter, and centimeter sticks unifix cubes base ten blocks

Quotient

The resulting number of groups

When children know the number 0-9 and can identify and write the respective numerals, they can participate in grouping activities. What are those grouping activities?

The size of groups The materials used The numbers of groups formed The manner of recording

To solve addition and subtraction problems using the base ten blocks, children exchange or trade a rod for ten units rather than "take apart" a rod.

True

When children first decode numbers, they are not likely to use the multiplicative term times; rather they talk about groups. For example, the 2 in 28 is explained as two groups of ten or two tens.

True

When solving division problems such as 56 divided by 5, the phrase "5 goes into 56" should not be used because it has no mathematical meaning.

True

Mark all that can be considered to be components that are important to keep in mind when teaching computational procedures to children.

Use estimation and mental computation. Use models for computation Pose story problems set in real-world contexts.

Nominal Numbers

Used to name objects

Mark all of what to do when teaching basic facts.

mark drill enjoyable. focus on self-improvement work on facts over time.

Read a short article (Links to an external site.) and answer the question below. Among phrases below, mark all that would be related more to place value and number sense?

"making 10" "regrouping" "trade tens for ones" "going to become"

Translation Problems

A school auditorium can seat 648 people in 18 equal rows. How many seats are there in each row?

Puzzles

Can you join all nine dots using four straight lines without your pencil from the paper?

What do we call this transitional step below when solving an addition problem, 28+34? 2 tens and 8 ones + 3 tens and 4 ones ------------------------------------ 5 tens and 12 ones or 6 tens and 2 ones or 62 This is called [ ]

Expanded Notation

According to CCSSM, to add and subtract within 20, you may use several strategies. One strategy is decomposing a number leading to a ten. Its example is "8+6 = 8+2+4 =10+4 = 14."

False

Children will replace 10 unit blocks with a "rod" to represent a two-digit number, a place-value mat (with headings) should be used rather than an organization mat (without column headings)

False

Mark if what a student says is true or false. This is the one with the ruler. Student says the line segment is 3 1/2 or that you cannot tell how long the green line is.

False

Poly's 1957 phases of problem solving consists of 1. understanding the problem 2. devising a plan to solve the problem 3. Reflecting on the problem and 4. Implementing the solution plan.

False

Application Problems

How much does the school board pay for electricity in a school year?

*Read the following division problems.Choose a problem whose remainder is simply left over and is not taken into account. Partial Credit

Mr. Pak has 21 marbles. He wants to share them equally among her 5 children so that no one gets more than anyone else. How many marbles should she give to each child?

Ten

One group of ten and zero ones

Hundred

One group of ten groups of ten

Children can be given a set of miniature dolls, small cars or other small objects and ask to record how many objects they have.

One-to-one correspondence

There are factors contributing to children's difficulties in problem solving. Which factor does the statement explain? Children's out of school experiences are varied; therefore, children develop various problem solving strategies.

Sociocultural Factors

Working backward

Problems of this type are often best solved by starting at the final situation and working backward to find the solution.

Vygotsky's instructional approach to learning and the gradual release

Scaffolding

Roger had 13 stickers. He gave some to Colleen. He has 4 stickers left. How many stickers did he gave to Colleen? Karla makes a set of 13 cubes. She slowly removes cubes one by one, looking at the cubes remaining in the initial set. When she has removed 6 cubes, she counts the cubes in the remaining set. Finding that she has 7 cubes left, she removes 3 more cubes and again counts the cubes in the remaining set. Finding that there are now 4 cubes left, she stops removing cubes and counts the 9 cubes that were removed. Karla then responds, "He gave her 9." The type of the problem in the video is Separate-Change Unknown and the kid in the video is using direct modeling

Separate-Change Unknown Direct Modeling

There were 8 seals playing. 3 seals swam away. How many seals were still playing?

Separate-Result Unknown

John had some cookies. He gave 7 cookies to Amit. Now John has 4 cookies. How many cookies did John have to start with?

Separate-Start Unknown

Have your students stand in a circle. Decide what number you're going to start with and what number you're going to skip by.

Skip Counting

Dividend

The total number to be divided up

If students think that solving problems means looking for key words, such as "of" meaning "times"

Then have students ask them to solve problems that include key words but are not solved in the way using traditionally key words would imply.

If students think that there is no relationship between the value of each place.

Then have students describe the values of adjacent places, for example, 1 ten is the same as 10 ones

Front ene-strategy or Front end strategy

This strategy focuses on the left most or highest place value digits

Special Number Strategy

This strategy involves looking for numbers that are close to special values that are easy to work with

Clustering Strategy

This strategy is used when a set of numbers is close to each other in value

Compatible Number Strategy

This strategy is used when kids adjust the numbers so that they are easier to work with

Select all that belong to ways to assess children's place-value understanding.

Using manipulatives to represent numbers Regrouping with tens and ones Understanding tens and ones

Once children have developed computational procedures, they need many activities that will help to consolidate their understanding and to develop proficiency in terms of accuracy and speed. Mark all activities that consolidate and enrich children's understanding.

Using riddles, games, puzzles, computer softwares

Logical Reasoning

When children state they solved a problem by thinking it through, encourage them to reflect on how they did it

Mark all that can be included in the blank. children should know to fluently add and subtract within 1000 using strategies and algorithms based on [ ].

the relationship between addition and subtraction properties of operation place vlaue

If students think that solving problems means just pulling out the number and doing something to them

then have students model the problem with a manipulative model

If students think that number that look different must have different values (for example, 23 and 1 ten and 13 ones)

then have students model two such numbers with a manipulative material, ask students to compare their values, and discuss why there numbers have the same value but look different.

If students think that numbers with the same digits have the same value (For example 23, and 32 or 15 and 150

then students have to model two such numbers with a manipulative material, ask students to compare their values