Math Test 1 ede

List the digits in the order in which students should learn to write them? What is this based on?

1472536908 The student learns straight lines first (1,4,7), then the student moves to the curves of letters with straight lines (2,3,5), then the student focuses on curves (6,9), then the student understands these skills full circle (0,8) The gradual learning of lines/shapes

Associative Property of Addition

Contextual problems adding three addends in different orders Ex. 3 + (2 + 4) = (3 + 2) + 4

Explain why "key words" should NOT be taught

It sends a wrong message about doing mathematics to our students. When they look at key words, they are not understanding the full meaning of the problem rather just looking for key words. They don't work with two-step problems or more advanced problems

Explain why and how ten frames should be used, stating specific groups of Basic Facts for Addition.

It's a representation for adding WHY: It is used so students can relate other numbers to 10. This helps build computation skills. Ten frames help students see the relationships among a number and ten, whether it is less than or more than HOW: With the chart with 10 squares and the squares get a dot. The dots represent numbers & it helps students recognize numbers using the anchor number 5 & 10.

Daisy Duck has several pots of flowers. After Donald gave Daisy 6 more pots of flowers, she had 15 pots of flowers. How many pots of flowers did Daisy have before Donald gave her any?

Join

I have 15 hamsters and there are 3 hamsters in each cage. How many hamster cages do I have?

Measurement

Algorithm

Traditional method which includes a rule or procedure in order to solve a problem

Direct Modeling Strategies

Using manipulative (Base 10 blocks, pictures, etc.) along with counting to represent meaning directly

How does the Number of the Day routine promote place value understanding?

Was given a numerical value (mine was 492); gave the number context (a referent), wrote the value in words using place value (four hundreds, 9 tens, 2 ones) and in expanded form (400+90+2 = 492); then found one and two more/less than; helped to see a number in a variety of contexts and used in different mathematical ways; helped build understanding of place value by relating it to the expanded form

What is computational estimation?

getting an approximation mentally

What is number sense?

well understood number meanings, multiple relationships among numbers, recognition of the relative magnitude of numbers, knowledge of the effect of operations on numbers, referents to measure things in the real world

What is computational fluency?

when students can complete computations mentally and quickly

Explicit Strategy Instruction

students learn a strategy, then explore and practice it

Be able to describe place value development (ideas of 10 of one thing is ONE of something else)

"ten ones makes one ten" two meanings of "ten"; three meanings of "hundred"

Three phases of Basic Facts:

1. Counting Strategies 2. Reasoning Strategies 3. Mastery

The Zero/Identity Property of Addition

Adding (or subtracting) zero to a number doesn't change its identity Ex. 3 + 0 = 3

What are the necessary behaviors associated with counting?

Assign each counted item only one counting word Demonstrate one-to-one correspondence Produce the list of counting words in order

Associative Property of Multiplication

Changing the grouping of three or more factors does not change the product. Ex. 3 x (2 x 4) = (3 x 2) x 4

Commutative Property of Multiplication

Changing the order of the factors does not change the product.

Vicky is picking out a new skateboard. They can be black, gray, tan, or dark brown, and the wheels can be yellow, purple, green, pink, or orange. How many different combinations does Vicky have to choose from?

Combinations

Minnie has 15 red marbles and some blue marbles. She has 13 more blue marbles than red ones. How many blue marbles does Minnie have?

Compare

don'ts" for teaching Basic Facts

Do NOT: use lengthy times tests use public comparisons of mastery proceed through facts in order from 0-9 move to memorization too soon work on all facts at once use facts as a barrier to good mathematics use fact mastery as a requisite for calculator use

Ex. 3 lines x 4 people = 12 people Ex. Anna has 2 packs of gum. If each pack contains 6 pieces of gum, how many pieces of gum does Anna have?

Equal Groups

Rounding

Ex. $23 to $20

Compatible Numbers

Ex. $23 to $25

Caleb and Joe both have marble collections. Caleb has 20 marbles. Joe has two times as many marbles than Caleb. How many marbles does Joe have?

Multiplicative Comparison

Join

Must have a physical action Are not only for addition problems Think about gaining from an initial total

seperate

Must have a physical action Think about giving away from the initial total

Compare

No action

Part-Part-Whole

No action Think about adding two separate things together to get one total

Invented Strategy

Nontraditional method not involving the use of manipulatives May include written recordings and mental methods Benefits of Invented Strategies for Students:

How are place value concepts evident in the 1-100 chart?

Notice that as the numbers in a row got greater, the amount of tens stayed the same, but the number of ones increased; and that as the numbers in a column got greater, the number of tens increased, but the number of ones stayed the same

Commutative Property of Addition

Pair contextual problems that have the same addends, just in different orders Ex. 3 + 2 = 5 and 2 + 3 = 5

Mickey Mouse has 4 cubes of swiss cheese and 7 cubes of cheddar cheese. How many cubes of cheese does Mickey have?

Part-Part-Whole

Gabrielle has 12 eggs in her refrigerator. She wants to cook eggs for 3 people. How many eggs can each person have?

Partition

Ex. Mrs. Smith is building a bench and needs 6 lengths of wood that each measure 1.4 meters. How many meters of wood does he need to purchase? Ex. 5 in. x 6 in. = 30 square inches

Product of Measures

List examples of the three kinds of Base-10 Models:

Proportional: Group able (Uni-fix cubes, Multi-link cubes) Pre-grouped (Base 10 blocks, flats, longs, units) Non Proportional: Teddy bear counters

Pluto gave Goofy 7 of his dog bones leaving him with 5 bones. How many bones did Pluto have before he gave any to Goofy?

Separate

List the skills/concepts that are taught through the Shapes of Numbers activity

Shapes of Numbers: Number sense Mickey Ticket to Class: Number sense

How should multiplication be introduced to students?

Start with repeated addition and then move on to invented strategies for multiplication Combinations is a good place to start Start with numbers 2 and 5

Equal Groups

The answer is the same type of thing as one of the numbers

Partition

The number of groups is known, but not the size of each group (dealing cards to a group of people)

Identity Property of Multiplication

The product of any number and 1 is that number.

Measurement

The size of each group is known, but not the number of groups

Combinations

The two numbers in a multiplicative problem represent different types of things; the answer will be a "new thing" (shirts and shorts combined form outfits) Mickey's Outfits Activity

Product of Measures

The two numbers in a multiplicative problem represent different types of things; the answer will be in terms of something different (a 5 INCH by 7 INCH frame frames a picture that is 35 SQUARE INCHES)

Distributive Property of Multiplication over Addition

a(b / c) = a times b plus a times c; add first & then multiply OR multiply each & then add Rule: a(b + c) = (a x b) + (a x c) Ex. 4 (2 + 3) = (4 x 2) + (4 x 3)

addition

addend + addend = sum

front-end estimation

an estimation method in which the front digits are added or subtracted Ex. $26 to $20

Guided Invention

an open-ended focus on strategies Students select a strategy based on their knowledge of number relationships

Division

dividend/divisor = quotient

Memorization

does not devote time to developing strategies

Know the "dos for teaching Basic Facts

emphasize operation sense, as it is very important in the mastery of basic facts ask students to self monitor focus on self-improvement drill in short time segments work on facts over time involve families make drill enjoyable use technology emphasize the importance of quick recall of facts

Multiplication

factor x factor = product

Multiplicative Comparison

involves the comparison of 2 quantities manipulatively, involves finding "how many times as much" of 1 quantity is compared in another quantity, or "stretching" the original by a certain quantity.

Subtraction

minuend - subtrahend = difference

Explain what a Basic Fact is

refers to mathematical relationships in which the two parts are less than 10.