Math 7813 extra questions
define measurement division
(also called repeated subtraction division), is a way of understanding division in which you divide an amount into groups of a given size. .. In the partitive interpretation, 4 is the number of objects in each group; in the measurement interpretation, 4 is the number of groups. In measurement division, the divisor names the size of the group (or unit), and the quotient represents the number of groups (or units). A measurement division problem can often be solved by thinking, "How many are in ?"
true" statements about multiplying whole numbers
-Multiplication is the same as repeated addition when you add the same number again and again. -Times means "groups of." -A multiplication problem can be shown as a rectangle. -You can reverse the order of the factors and the product stays the same. -You can break numbers apart to make multiplying easier. -When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one.
true" statements about dividing whole numbers
-Switch the numerator and denominator of the fraction you are dividing by. -Multiply the two fractions together. -Simplify your answer if needed.
Multiplicative comparison problems usually use phrases like:
-Times as many (3 times as many candies) -Times more (5 times more apples) -Times as much (7 times as much as the blue ribbon) -Times as large (10 times as large as a brick)
Little cube or on manipulative block represents
0.001 or 1/1000
big cube manipulative represents
1 whole or 1.00
Example of cardinal numbers
1(one), 2(two), 3(three)
1 km equals how many meters
1,000 m
1 meter equal millimeters
1,000 mm
flat manipulative represents
1/10 or 0.1
10 rod equals represents
1/100 or 0.01
How many flat manipulative does it take to make a big cube / 1 whole
10 flats because 0.1x10=1 whole
1 cm equals how many millimeters
10 mm
1 meter equal how many centimeters
100 cm
how many ten rods does it take to make a big cube / 1 whole
100 ten rods
What are ordinal numbers from 1 to 10?
1st - First, 2nd - Second, 3rd - Third, 4th - Fourth, 5th - Fifth, 6th - Sixth, 7th - Seventh, 8th - Eighth, 9th - Ninth and 10th - Tenth respectively.
Example of ordinal number
1st(first), 2nd(second), 3rd(third)
examples of prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23
What is the greatest common factor of 12 and 9
3
There are 3 apples and 4 lemons. What the ratio as a fraction.
3/7 are apples and 4/7 are lemons
What is the least common multiple of 9 and 12?
36
There are 3 apples and 4 lemons. What is the ratio of apples to lemons?
3:4
What number is the subtrahend of 9-4=5?
4
Examples of composite numbers?
4,6,8,9,10,12,14,15,16,18,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36
There are 3 apples and 4 lemons. What is the ratio of lemons to total fruit?
4:7
What is the difference of 9-4=5?
5
What is the greatest common factor of 20 and 15
5
A rectangular prism has
6 faces. They are all rectangles. Faces are flat surfaces of a three-dimensional shape. It is not a cube. All faces of a cube are squares. On this shape, they are not.
A cube has
6 faces. They are all squares.
What is the least common multiple of 12 and 20
60
What number is the minued of 9-4=5
9
Ratios can be shown in different ways:
:•to separate example values• using the "/" to separate one value from the total • as a decimal, after dividing one value by the total • as a percentage, after dividing one value by the total
less than symbol
<
greater than symbol
>
Example of a multiplicative comparison problem using the equation:
A building is 18 feet tall and the building is three times Jerry's height. How tall is Jerry? Let Jerry's height be "h" Height of the building = 18 ft which is 3 times Jerry's height, that is, 3 times h Therefore, 18 = 3 × h Dividing both sides by 3, we get: 18 ÷ 3 = 3 × h ÷ 3 6 = h h = 6 ft Hence Jerry is 6 ft tall.
definition of a parallelogram?
A flat shape with 4 straight sides where opposite sides are parallel. Also: • opposite sides are equal in length, and. • opposite angles are equal (angles "A" are the same, and angles "B" are the same) NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
Expression
A math phrase, no equal, variable can change. For example, x+7 or 3D (means times) and 5+7 or 3x11
Divisor
A number by which another number is to be divided.
Dividend
A number to be divided by another number.
What is a comparison using division?
A ratio is a comparison of two numbers by division. The value of a ratio is the quotient that results from dividing the two numbers. For example, the value of the ratio 35:7 is 5, which you find by computing 35 ÷ 7 = 5.
What is the definition of a ratio?
A relationship between different amounts or the relative sizes of two or more values. A comparison of two values
Variable
A symbol used to represent an unknown value. For example, x, y or etc. In addition, x + 7 can be 3+7 or 5+7
define trapezoid
A trapezoid is a quadrilateral with at least one pair of parallel sides. No other features matter. (In English-speaking countries outside of North America, the equivalent term is trapezium.) The parallel sides may be vertical , horizontal , or slanting . A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.
define right angled triangle
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.
What is an equilateral triangle always an example of?
An acute triangle is a triangle in which each angle is an acute angle. Any triangle which is not acute is either a right triangle or an obtuse triangle. All acute triangle angles are less then 90 degrees. For example, an equilateral triangle is always acute, since all angles (which are 60) are all less than 90.
Define equilateral triangle
An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal.
Which property of addition is shown? 1 + (4 + 2) = (1 + 4) + 2
Associative property: (r + s) + t = r + (s + t) You can group the addends with parentheses and get the same sum.
What is the rule for an isosceles triangle?
Basic Properties. Because angles opposite equal sides are themselves equal, an isosceles triangle has two equal angles (the ones opposite the two equal sides). Thus, given two equal sides and a single angle, the entire structure of the triangle can be determined.
Which equation shows the commutative property of addition?
Commutative property: m + n = n + mYou can add numbers in any order and get the same sum. 5 + 6 = 6 + 5 This equation shows the commutative property. The order of the addends is changed.
What is the difference between composing and decomposing numbers?
Compose: To compose in math is putting a number together using its parts. Decompose: To decompose in math is to break down numbers into parts. Add: To add is to join two numbers together. Subtract: To subtract is to take away from another to see the difference.
What is the purpose of decomposing numbers?
Decomposing is breaking a number into parts. Students are used to working with whole numbers (using objects to make 5) and will now learn that numbers can be broken into parts (2 and 3 is the same as 5). They will decompose numbers drawing and using objects.
Example of an additive comparison
Example of an additive comparison problem using the equation is given. Aaron takes 16 minutes to reach school from his home. Ryan takes 5 more minutes than Aaron and Sheryl takes 3 more minutes than Ryan. ... Therefore, Sheryl takes 24 minutes to reach school.
What place value is the 6 in 657,890,123
Hundred millions
What place value is the 9 in 987,125?
Hundred thousandths
What place value is the 1 in 657,890,123
Hundreds
What place value is the 7 in 6584791.0324
Hundreds
What place value is the 8 in 657,890,123
Hundreds thousands
What place value is the 3 in 6584791.0324
Hundredths
Which property of addition is shown? 5 = 0 + 5
Identity property
define pentagon
In geometry, a pentagon is a five-sided polygon with five straight sides and five interior angles that sum up to 540° . A pentagon shape is a plane figure, or flat (two-dimensional) 5-sided geometric shape.
Measurement model example
Measurement example: A pencil costs 8 cents. How many pencils can I buy for 24 cents? The total cost is again divided among several pencils, but this time the price for one pencil is known, and the number of pencils (groups) in unknown.
What place value is the 6 in 6584791.0324
Millions
Multiplicative comparison example
Multiplication example: A farmer has 6 ducks. He has 3 times as many chickens as ducks. How many chickens does he have? Partitive example: A farmer has 3 times as many chickens as ducks. He has 18 chickens How many ducks does he have? Measurement example: A farmer has 6 ducks and 18 chickens. The farmer has how many times as many chickens as ducks?
What place value is the 7 in 657,890,123
One million
One-to-one Correspondence
One such principle is known as one-to-one correspondence. It's the idea that numbers correspond to specific quantities. For example, in playing a game, a child counts 1, 2, 3, 4, 5 dots on the die and jumps 1, 2, 3, 4, 5 spaces on the board because 5 dots correspond in quantity to 5 jumps. is an early learning math skill that involves the act of counting each object in a set once, and only once with one touch per object.
What place value is the 1 in 6584791.0324
Ones
What place value is the 3 in 657,890,123
Ones
Define perimeter, area and volume.
Perimeter, distance around a two dimensional object. Area, space within a two dimensional object, expressed as a unit of measurement squared, square feet or square inches; Volume, space contained within a three dimensional object. Expressed as a cubed unit, such as cubic feet or cubic inches
define rhombus
Rhombus is a special type of a parallelogram whose all sides are equal. The difference between a square and rhombus is that all angles of a square are right angles, but the angles of a rhombus need not be right angles. So, a rhombus with right angles becomes a square.
Why is composing and decomposing numbers important?
Students who are able to fluently decompose quantities and then compose quantities are able to adapt their calculations to different sets of numbers. Decomposing larger numbers by place value is also an important concept and skill that students can use when adding, subtracting, multiplying and dividing.
What place value is the 8 in 6584791.0324
Ten thousands
What place value is the 4 in 6584791.0324
Ten thousandths
What place value is the 0 in 6584791.0324
Tenths
What is cardinality?
The idea that the final number of the sequence represents the amount of objects that were counted
minued
The number that is to be subtracted from.
ordinal numbers examples
The numbers 1st(First), 2nd(Second), 3rd(Third), 4th(Fourth), 5th(Fifth), 6th(Sixth), 7th(Seventh), 8th(Eighth), 9th(Ninth) and 10th(Tenth) tell the position of different floors in the building. Hence, all of them are ordinal numbers. E
Define ordinal numbers
The numbers which give us the exact position of an object are ordinal numbers. Ordinal numbers tell the position of an object rather than their quantity
Define cardinal numbers
The numbers which give us the exact quantity of an object are called cardinal numbers. In other words, cardinal numbers answer how many.
example of ordinal number
The picture of a building showing different floors number(1st(first), 2nd(second), 3rd(third)). We can use ordinal numbers to define their position.
Quotient
The result obtained by dividing one number by another number.
Why are they like terms?
The variable part has to be the same note the numbers. For example, 2XY + -1X2Y
Why are they unlike terms?
The variables are different The exponents are different one term is a constant and the other has a variable
What is a composite number?
There are multiple factors
What are the types of polygon?
There are two main types of polygon - regular and irregular. A regular polygon has equal length sides with equal angles between each side. Any other polygon is an irregular polygon, which by definition has unequal length sides and unequal angles between sides.
What is making ten strategies
To use the strategy, students decompose one of the addends to make a ten from the other. For example, 8+4= put 8 in the one ten frame and 4 in another 10. Next, decompose 4 which is 2 and 2. After that, move to over two to the ten frame with 8. Now it makes 10. The new problem it 10+2 which makes it easy to solve.
unlike terms
Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. ... Since the coefficient doesn't affect likeness, all constant terms are like terms.
What is Partitive model of division?
When dividing a number into a known number of groups. For example, when we divide 8 into 2 groups and we want to determine how many items each group will have. Also known as fair share division since you are dividing up the quantity evenly amongst each group.
How do you know when numbers are multiples of 3, 6, 7, 10, and etc.
When the given number can be divided or are a product of of a given number. For example, multiples of 6. 6*1, 6*2, 6*3 and etc. (if 6 can be divided into the answer than it is a multiple of 6). Yes, zero is a multiple of every number. So, 0 is a multiple of 6. Also, 6 x 0 = 0.
Is this an example of an equation 7 × 6 = 42, yes or no
Yes
What is one rule with multiplying fraction
You don't need a common denominator
define square
a flat geometric figure that has four equal sides and four right angles. 2 : something formed with four equal or roughly equal sides and four right angles the squares of a checkerboard. 3 : the product of a number or amount multiplied by itself.
ordinal numbers
a number defining a thing's position in a series, such as "first," "second," or "third. an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
What model is this: -Arthur divided 𝟑 𝟒 of his kingdom into parcels of land, each being 𝟏 𝟖 of the entire kingdom. How many parcels did he make? -Number Line: Molly's friend, Xavier, also has 𝟏𝟏 𝟖 cups of strawberries. He needs 𝟑 𝟒 cup of strawberries to make a batch of tarts. How many batches can he make? Draw a model to support your solution. -Bonnie Baker has a total of 1/2 pound of chocolate. She needs 1/8 pound of chocolate for each batch of brownies she bakes. How many batches of brownies can Bonnie bake with 1/2 pound of chocolate? -Joe is making chocolate fudge and the recipe calls for 3 1/4 cups of sugar. Joe uses a 1/4 cup measuring the sugar. How many times does joe need to fill the measuring cup to measure the sugar needed for the recipe? - A trail is 3 1/4 mile long and trail markers are placed at 1/4 mile intervals along the trail. How many trail markers are placed along the trail? a. measurement model b. partitive model
a. measurement model
What is a polygon
any shape made up of straight lines that can be drawn on a flat surface, like a piece of paper. Such shapesinclude squares, rectangles, triangles and pentagons but not circles or any other shape that includes a curve.
Part-whole relationships
are important for learning about number as they develop the understanding of how numbers are made up of other numbers. That is, numbers can be partitioned into smaller constituents in the same way that 8 can be made up of 2 and 6.
like terms
are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only like terms can be combined.
Which property of addition is shown? (6 + 3) + 2 = 6 + (3 + 2)
associative property
What model is this: -There are 24 flowers equally distributed in 8 vases. ... Again, place 1 flower in each group. After placing the last 8 flowers in the 8 groups, we are left 8 - 8 = 0 flowers -10 divided into 5 groups gives a result of ___ per group (answer 2 per group) - 3 1/4 cups of fills 1/4 of a container. How many cups of soup will it take to fill the whole container? a. measurement model b. partitive model
b. partitive model
for example a student can be given 89, 708, 37, and 93 to put in order from least to greatest and provide an explanation. What strategy is this?
benchmark strategy
Benchmark Strategy
benchmarks can be defined as the standard or reference point against which something can be measured, compared, or assessed. Benchmark numbers are numbers against which other numbers or quantities can be estimated and compared. Benchmark numbers are usually multiples of 10 or 100.
Which property of addition is shown? 2 + 7 = 7 + 2
commutative property Commutative property: d + f = f + dYou can add numbers in any order and get the same sum.
Multiplicative comparison means
comparing two things or sets that need multiplication.. For example, Sam has twice as many balloons as Sid has. Sam has twice as many balloons as Sid has. Problems for multiplicative comparison are generally word problems and can be solved forming an equation.
what strategy is this: what is the answer to 5+2. A student starts with the number 5 and say 6, 7
counting on
A line
goes without end in both directions.
A ray
has 1 endpoint and goes without end in 1 direction
A pyramid has
has one face as a base. The base is a triangle. triangle. The other 3 faces are all triangles. These triangles meet at a vertex. Faces are flat surfaces of a three-dimensional shape.
symmetry
having the same shape, size, and position on both sides of a dividing line. For instance, if folded the lines will match evenly
Keyword for measurement model
how many times intervals
What place value is the 1 in 987,125?
hundreds place
Example of Ratios
if there is 1 boy and 3 girls you could write the ratio as: -1:3 (for every one boy there are 3 girls) -1/4 are boys and 3/4 are girls -0.25 are boys (by dividing 1 by 4) -25% are boys (0.25 as a percentage)
Define Isosceles Triangle
in geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case
What is verbal counting?
involves a child learning a list of number words. While counting to large numbers it requires a system in order to keep track. This system is called Hindu-Arabic numeral system and it is based on two ideas.
counting on or counting strategy
is a beginning mental math strategy for addition. ... Counting on means that you start with the biggest number and then count up from there. For example, to add 5+3, start with the "5" and then count up, "6, 7, 8." This is to discourage students from counting like this: "1, 2, 3, 4, 5
quadrilateral
is a polygon with 4 sides and 4 corners. The word 'quadrilateral' comes from 'quad' meaning '4' and 'lateral' meaning 'of sides'. The interior angles of quadrilaterals add to 360 degrees. Any quadrilateral with 4 right angles is a rectangle.
Double plus one
is a strategy used to add two consecutive numbers that is, when they are next to each other. We simply add the smaller number twice or doubleit and then, add 1 to it, to get the final result.
Rote counting
is simply saying the numbers in order, usually starting with one, e.g. 1,2,3,4,5 etc. ... How do you teach rote counting? Teach rote counting with simple songs that count upwards. Counting simple actions and objects that appear throughout everyday life is also recommended, for example counting stairs.
define place value strategy
is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that whilst a digit can be the same, its value depends on where it is in the number.
What is a prime number?
it only has 1 and itself as factors
Perimeter of a rectangle =
length + width + length + width
Area of a rectangle =
length × width
Perpendicular
lines meet at right angles. They make square corners.
halving and doubling
means simply half one of the factors and double the other. Take this example. To solve 25×16, we could double the 25 to make 50 and then half the 16 to make 8.
Counting up
method involves viewing a subtraction problem from a perspective that focuses on adding. Write out your subtraction problem. For example, you may have 327 - 168. Figure out what must be added to the ones column of the smaller number to reach the next 10s number.
You can make equivalent fractions by
multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.
A sphere has
no flat surfaces. It's completely round.
A cone has
one face. It is a circle. The rest of the shape is curved.
What strategy is this? For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000.
place value strategy
rote counting
reciting numbers in order without understanding that each number represents a specific amount
A line
segment has 2 endpoints. A line never ends
An equation is
shows that two amounts are equal.
counting-up subtraction
subtraction strategy in which the answer is found by "counting up" from the smaller number to the larger number
Define quotient
the answer to a division problem
Define sum
the answer to an addition problem
Congruent figures have
the exact same size and shape. Even when reflected, rotated, or translated, their size and shape remain identical. Answer: Triangle EFG is reflected across the x-axis so that one triangle shows a mirror image of the other.
subtrahend
the number being subtracted
A cylinder has
two faces. They are both circles. The rest of the shape is curved. Faces are flat surfaces of a three-dimensional shape.
additive comparison means
we find the relation between two amounts by asking or tellinghow much more is one compared to the other.
Define proportion
when two ratios are equal
Measurements model of division with fractions
when using the measurement model of division, we are asking how many of the divisor (the second fraction) are in the dividend (the first fraction). The quotient tells us the number of copies of the divisor that are in the dividend.
partitive division means
you know the total number of groups, and are trying to find the number of items in each group.
