"Elementary and Middle School Mathematics: Teaching Developmentally" is a widely used textbook for teaching math at elementary and middle school levels.
What is developmentally ?
In education, the term "developmentally" refers to the idea that students should be taught in a way that is appropriate for their developmental level. Developmental teaching is a student-centered approach that takes into account the students’ abilities, interests, and needs as they learn.
Elementary and Middle School Mathematics: Teaching Developmentally is a textbook that provides an overview of the principles and practices of teaching mathematics in the elementary and middle school levels. It is designed to help teachers understand the mathematical concepts and skills that students need to learn at each grade level, as well as the best ways to teach those concepts and skills. The book covers a wide range of topics, including number sense and operations, algebra, geometry, measurement, and data analysis. It also provides strategies for differentiating instruction, using technology, and assessing student learning. The book is written by John A. Van de Walle and Karen S. Karp, and it is widely used as a textbook for teacher education programs and professional development workshops.
"Elementary and Middle School Mathematics: Teaching Developmentally" is a widely used textbook for teaching math at elementary and middle school levels.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The required equation that has solution as x = -2 and x = 2, are x²– 4 = 0 and 4x² = 16
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
x²– 4 = 0
x² = 4
x = ±2
4x² = 16
x² = 4
x = ±2
Thus, the required equation that has solution as x = -2 and x = 2, are x²– 4 = 0 and 4x² = 16
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Please answer the following question
Answer:
12
Step-by-step explanation:
Find the midpoint of the segment with the following endpoints.
(−4,−9) and (4,−1)
Answer:(0,-5)
Step-by-step explanation: to start you add both x’s together then divide by two so you get 0 then you add both of the y’s together divide by 2 and you get -5 the answer you got from the x’s goes first then the answer from the y’s hence (0,-5)
what is $\frac{0.\overline{3}}{0.8\overline{3}}$? express your answer as a common fraction in lowest terms.
0.833333... as a common fraction is 5/6
Let x= 0.833...
then 10x = 8.333...
so, 10x -x = 8.333..-0.833..
9x= 7.5
multiplying both sides by 0
90x= 75
x=75/90
x=5/6
Therefore, 0.833333... as a common fraction is 5/6
Decimal is a system of numbers in mathematics used to denote arithmetic based on the tenth part or powers of ten. It is denoted by a point".". It is also used for a fraction whose denominator is a power of ten and whose numerator is expressed in numbers beside the decimal point of 10. It is also used to denote improper fractions in numerical. E.g- 2/10=0.2
Fractions in mathematics are a part of whole. There are four types of fractions: proper, improper, simple, and complex. It has two parts Numerator and denominator.
Complete question- How do you convert 0.83 (3 repeating) to a fraction?
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How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points 0 comma 2 and 2 comma 1. No solution Infinitely many solutions One solution at (2, 0) One solution at (0, 2)
The graph represented is a single line and the solution is
Infinitely many solutionsHow to determine the solution of a single lineThe solution of a sets of linear equations is determined as follows
The location where the lines intersect will be the only solution if they intersect. If they run parallel, there won't be any solution. There will be numerous (infinite) solutions if they are on the same line.Since the coordinates are for a line hence it represents lines on the same line and this results to infinitely many solution
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Answer:
Infinite solutions
Step-by-step explanation:
Got it right on the test
Select the correct answer from each drop-down menu.
1. If , _____ then ∆ABC and ∆DEF are congruent by the ASA criterion.
A.) AB=DE
B.)CA=FD
C.)Angle B is congruent to angle E
D.)Angle A is congruent to angle D
2. If , ______ then ∆ABC and ∆DEF are congruent by the SAS criterion.
A.) AB=DE
B.)CA=FD
C.)Angle B is congruent to angle E
D.)Angle A is congruent to angle D
3. ∆ABC and ∆DEF are congruent if
A.) Angle A is congruent to angle D
B.) AB=DE
C.) AB=DF
ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.
What is congruent ?
In geometry, congruent refers to the condition where two or more figures have the same size and shape. Congruent figures have the same dimensions, angles, and proportions. Two figures are congruent if they can be superimposed exactly on each.
1) If, C.) Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.
2) If, D.) Angle A is congruent to angle D then ∆ABC and ∆DEF are congruent by the SAS criterion.
3) ∆ABC and ∆DEF are congruent if B.) AB=DE
ASA criterion: If in two triangles, two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.
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Is it possible to form a right triangle with the sides as 15 cm 8 cm and 17 cm?
No, it is not possible to form a right triangle with the sides as 15 cm, 8 cm, and 17 cm .
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) must equal the square of the longest side (the hypotenuse). In this case, 15^2 + 8^2 = 289 + 64 = 353, which is not equal to 17^2 = 289.
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Find the equation of a line parallel to y=-x+7 that passes through the point (4,5).
Answer Y=-X+9
Step-by-step explanation:
Desmos Calculator.
Here, both equations are graphed and the answer is shown going through the required coordinate.
Which has to be true in order for this comparison to be made?
A Three hundredths is larger than three tenths.Three hundredths is larger than three tenths.
B Three tenths is larger than four tenths.Three tenths is larger than four tenths.
C Five hundredths is larger than four hundredths.Five hundredths is larger than four hundredths.
D Five hundredths is larger than 4 tenths.
Answer:
C. Five hundredths is larger than four hundredths.Five hundredths is larger than four hundredths.
Answer:
C
Step-by-step explanation:
A
[tex] \frac{3}{100} < \frac{4}{10} \times \frac{10}{10} = \frac{40}{100} [/tex]
B
[tex] \frac{3}{100} < \frac{3}{10} \times \frac{10}{10} = \frac{30}{100} [/tex]
C
[tex] \frac{5}{100} > \frac{4}{100} [/tex]
D
[tex] \frac{5}{100} < \frac{4}{10} \times \frac{10}{10} = \frac{40}{100} [/tex]
Help please thank you
the ordered pair givien in the first row in the table can be written using function notation as f(1)=-2
Answer: Yes, that is correct.
The ordered pair (1,-2) can be written using function notation as f(1) = -2.
The first number in the ordered pair, 1, is the input value and the second number, -2, is the output value. The function notation f(x) is used to indicate that the output value is a function of the input value x.
In this case, f(1) = -2 means that when the input value is 1, the output value is -2. This can be represented as a point (1,-2) on the coordinate plane.
Step-by-step explanation:
Which question should you expect to be answered with variable data?
A. How tall are the students in my class?
B. How many phone calls did I make yesterday?
C. What was the highest grade on the last history test?
D. How many people attended the last middle school volleyball game?
B, C, and D are all questions that should be expected to be answered with variable data
Which questions are to be answered with variable data?Variable data refers to information that can change or vary, as opposed to fixed or constant data. In the context of statistics and data analysis, variable data refers to data that can take on different values for different individuals or observations.
B, C, and D are all questions that should be expected to be answered with variable data because the answer to each of these questions can change depending on the specific context or situation.
For example, the number of phone calls one makes on a given day can vary, the highest grade on a test can change from test to test, and the number of people who attend a volleyball game can also change.
A. How tall are the students in my class? is a question that should be expected to be answered with fixed data as the height of the students in the class will stay the same unless there is a significant change in their height.
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a furniture company manufactures dining room tables and chairs. each table requires 8 hours from the assembly department and 2 hours from the finishing department and contributes a profit of $90. each chair requires 2 hours from the assembly department and 1 hours from the finishing department and contributes a profit of $25. the maximum labor hours available each day in the assembly and finishing department is 400 and 120. how many chairs and tables should be manufactured to maximize and minimize the daily profit?
To maximize the profit only 52 Tables must be manufactured daily and to minimize the profit only 173 chairs must be manufactured working with the efficiency given.
What is efficiency?
The ratio of work accomplished by a machine or process to total energy expended or heat consumed is known as efficiency.
Efficiency refers to how close we can get to a specific outcome from a given input with the least amount of waste. Efficiency is the capacity to waste as little material, work, energy, and time as possible when executing a task or generating a desired outcome.
The ratio of usable output to total input can be used to calculate efficiency. The efficiency of a device is defined as the ratio of energy transferred to a usable form to the total energy provided originally.
Now
For table,
assembly hours=8
finishing hours = 2
profit/table=$90
For Chairs
assembly hours=2
finishing hours = 1
profit/chair=$25
Total assembly hours in a day=400
Total finishing hours in a day=120
As profit for table is more than profit for chair. Therefore, for maximum profit only Tables will be manufactured and will be
=total hours available/Time taken for one chair
=520/10
Tables manufactured=52
and for minimum profit only chairs will be manufactured
=520/3
chairs manufactured=173
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d the length of the third side. If necessary, round to the ne
12
14
The answer is 13. The Pythagorean theorem can be used to determine the hypotenuse.
What is the length of the 3rd side?A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. The answer is 13. The Pythagorean theorem can be used to determine the hypotenuse.The theorem informs us that if we designate that side as side "c"
c² = 5² + 12²\s c² = 25 +144 = 169\s c = √169 = 13
The third side measures 13 units in length.
Further commentary
The three digits (5, 12, and 13) form a "Pythagorean triple."
They can be utilized to create a right triangle because they are integers.
The triples (3, 4, 5), (7, 24, 25), and (8, 15, 17) are other triples that are frequently encountered in algebraic problems.
It might be worthwhile for you to keep these in mind.
The third side is 13 when you observe side lengths of 5 and 12, therefore you don't need to do any math to determine this.
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The cost of each white tile was £2
The cost of each blue tile was £4
b) work out the radio of the ratio of the total cost of the white tiled to the total of the blue tiles
The ratio of the total cost of the white tile to the total of the blue tiles will be 3/2.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Ewen has 48 white tiles and 16 blue tiles. The cost of each white tile was £2. The cost of each blue tile was £4.
The ratio of the total cost of the white tiled to the total of the blue tiles will be given as,
Ratio = (2 x 48) / (4 x 16)
Ratio = 96 / 64
Ratio = 3 / 2
The ratio of the total cost of the white tile to the total of the blue tiles will be 3/2.
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The missing part of the question is given below.
Ewen has 48 white tiles and 16 blue tiles.
if f(x) = x^2 - 6 and g(x) = 2x + 1, WHICH EXPRESSION IS EQUIVALENT TO (F O G)(X),
The solution for F(g(x) will be equal to 4x² + 4x - 5.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the function f(x) is x² - 6 and the function g(x) is 2x + 1. The value of the function F(g(x) will be calculated as,
F(g(x) = ( 2x + 1 )² - 6
F(g(x) = ( 4x² + 4x + 1) - 6
F(g(x) = 4x² + 4x - 5
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Attendance at literacy night was 55% of attendance at the concert. How many people at literacy night
On solving the provided question, we can say that the 70 percentage of the people attended the music concert also attended the drama play
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Drama:
[tex]50 x 350/ 100 = 175 \\\ 350 / 2 (50percent ) = 175\\\50percent (1/2) of 350 = 175\[/tex]
Music Concert:
[tex]175/250 x 100% = 70percent \\175 of 250 = 70percent[/tex]
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You have $5.00 and you need to make copies of a flyer at a store that charges $0.30
per copy. Find the inequality that represents the number of copies you can make. Use
x as the variable.
What is the maximum number of copies you can afford to make?
Answer:
The required number maximum number of copies can be afforded x < 24.28.
Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.
What is inequality?
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of copies be x,
According to the question,
0.35x < 8.50
x < 8.50 / 0.35
x < 24.28
Thus, the required number maximum number of copies can be afforded x < 24.28.
Step-by-step explanation:
I NEED HELP ILL GIVE BRAINLIEST|
The cost of new cars and trucks are expected to increase `2.9\%` next year.
Write an equation that will help calculate the cost of other cars next year.
Use `t` to represent this year's cost and `n` to represent next year's cost.
The equation n = t * 1.029 represents the cost of new cars and trucks next year.
What is the percent increase?
The percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. Mathematically, the formula is expressed as Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.
The 2.9% increase in cost is represented by the factor of 1.029 (1 + 0.029). To calculate the cost of a car next year, we multiply this year's cost (t) by 1.029.
n = t * 1.029
Where n represents next year's cost and t represents this year's cost.
This equation can also be written as n = t(1 + 0.029) or n = t + 0.029t which shows the relationship between this year's cost and next year's cost.
Hence, The equation n = t * 1.029 represents the cost of new cars and trucks next year.
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how many terms of the sequence $\sqrt{1},\sqrt{2},\sqrt{3},\sqrt{4},\ldots$ are less than or equal to $20$?
Answer:
i want points
Step-by-step explanation:
get scamed
jim drinks 15 ounces of water each hour. which expression shows how much he drank
The amount of water drank in 12 hours will be 180 ounces.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jim drinks 15 ounces of water each hour. The amount of water drank by Jim in 12 hours will be,
Amount of water = 15 x 12
Amount of water = 180 ounces
Hence, the amount of water drank in 12 hours will be 180 ounces.
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Please help its finals
The number of people in attendance who would prefer chili on a hotdog is 3,380.
Option B is the correct answer.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of attendance = 8450
Number of people who prefer chili on a hotdog out of 150.
= 60
The percentage of people who prefer chili on a hotdog out of 150.
= 60/150 x 100
= 40%
Now,
The number of people who prefer chili on a hotdog from 8450 attendance.
= 40% of 8450
= 40/100 x 8450
= 3380
Thus,
3,380 in attendance would prefer chili on a hotdog.
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i need help please.please show WORK
Answer:
Step-by-step explanation:
Colin deposited $1,230 in an account that pays 3.19% simple interest for three years.
a. What will the interest be for the three years?
b. What will be the new balance after three years?
The interest after three years is $117.711 and new balance after three years is $1347.711
How to determine the interest for the three years?Simple interest is a type of interest calculated on the initial principal or starting amount of a loan or investment.
The formula for simple interest is:
I = PRT/100
Where:
I = Interest
P = Principal or starting amount
R = Interest rate
T = Time
a. Interest after three years:
I = PRT/100
P = $1,230, R = 3.19% and T = 3 years
I = (1,230 ×3.19 × 3)/100
I = $117.711
b. New balance after three years:
New balance = P + I
New balance = $1,230 + $117.711 = $1347.711
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Rebecca carries a balance on her credit card each month. Today is the first day of the new. 28-day billing cycle. The current balance is x and the APR is 24%.
Rebecca is buying a friend an expensive gift that costs $1,400 that she plans to put on her credit card. This will be her only purchase this month. Sed she will be
making this purchase on the last day of the month. Part A if her finance charge will be $51 write and solve an equation to determine her current balance on her credit card show your work. Part B How much in finance charges can she save by making the purchase on the last day of the billing cycle
Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.
Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.
How do equations work?
A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.
Equation symbols (=) are used to represent equations.
A finance charge is what?
The interest and other fees levied on credit cards are included in a finance charge.
Typically, the finance charge is based on a stated APR (annual percentage rate).
The month's billing cycle lasts for 28 days.
Balance at current starting = x.
APR = 24%, or annual percentage rate.
The monthly percentage rate (MPR) equals 2% (24% divided by 12).
The final day's purchase cost $1,400.
$51 is the total finance fee for the month.
($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.
$50 ($51 - $1) serves as the initial balance's finance charge.
The starting balance at this time is x = $2,500 ($50 x 2%).
Current Beginning Balance Equation: x = 51 - 1 0.02
($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.
Finance charge savings from buying on the last day equals $27 ($28 - $1).
By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.
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How many 0.5 inch cubes will fill the rectangular prism with side lengths of 3inches by 7.5 inches and 4 inches?
The number of cubes that can be filled in the rectangular prism is 720.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Volume of a rectangular prism = Length × Width × Height
Given a rectangular prism with side lengths 3inches by 7.5 inches and 4 inches.
Volume of rectangular prism = 3 × 7.5 × 4 = 90 inches³
Volume of a cube = (side length)³
Given cube has side length 0.5 inch.
Volume of cube = (0.5)³ = 0.125 inches³
Number of cubes that can be filled in the rectangular box = 90 / 0.125
= 720
Hence 720 cubes can be filled in the rectangular prism.
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How many planes of symmetry does this sphere have? one two four infinitely many
Answer:
infintely many
Step-by-step explanation:
Simplify p2q6r8 / pq2r4
How do you write an algebraic expression from a word problem?
Step 1: Read through the word problem, and define your variables for any unknown quantities.
Step 2: Based on the problem, determine which mathematical operations will be used and on which numbers and variables.
Step 3: Put everything together into an expression that gives a solution to the word problem.
The cost of admission to a popular music concert was $162
for 12
children and 3
adults. The admission was $122
for 8
children and 3
adults in another music concert. How much was the admission for each child and adult?
1 . Understand the problem:
The admission cost for 12
children and 3
adults was $162.
The admission cost for 8
children and 3
adults was $122 .
2 . Translate the problem to an equation.
Let x
represent the admission cost for each child.
Let y
represent the admission cost for each adult.
The admission cost for 12
children plus 3
adults is equal to $162 .
That is, 12x+3y=162.
The admission cost for 8 children plus 3 adults is equal to $122.
That is, 8x+3y=122 .
3. Carry out the plan and solve the problem.
Subtract the second equation from the first.
12x+3y=162 8x+3y=122−−−−−−−−−−−− 4x = 40 x=10
Substitute 10
for x
in 8x+3y=122.
8(10)+3y=12280+3y=1223y=42y=14
Therefore, the cost of admission for each child is $10
and each adult is $14 .
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Jenny’s garden is 28 feet by 50 feet. What is the area of her garden? How could she use mental math to find the area?
Answer:
1400 square feet
Step-by-step explanation:
The area of a rectangle is found by multiplying its length by its width. So the area of Jenny's garden, which is 28 feet by 50 feet, is:
28 x 50 = 1400 square feet
To use mental math, Jenny could use the distributive property of multiplication.
First, she could break down the 28 into 20 and 8, and 50 into 40 and 10.
Then, she could think 20 x 50 = 1000 and 8 x 10 = 80
Finally, she could add 1000 + 80 = 1080.
So, the area of the garden can also be found by breaking down one of the dimensions into smaller parts, multiply them and add the results.
Another way to use mental math is to think of it as a square with side length of 50 ft, and then think of it as 28 rectangles of 1 ft by 50 ft. The area is then 50 x 28 = 1400 sq ft.