4th Grade - Make And Check Precise Calculations

 
     
 
     
 
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4th
Problem Solving
Make and Check Precise Calculations
Make precise calculations and check the validity of the results from the context of the problem.
Solve mathematical problems correctly and check your work cy following the procedures necessary for the problem (i.e. algorithms and models).
 

Sample Problems

(1)

Correct the quotient: Check if the estimate is too high, too low or accurate and choose the explanation. Calculate to find the accurate answer.

___5_R46

18) 136

- 90

46


  1. The estimate is too high because the product 90 is greater than the dividend.

  2. The estimate is too low because the difference of (136 – 90 = 46) is greater than the divisor.

  3. The estimate is accurate because the difference is less than the divisor. Correct remainder.


(b; the correct answer is 7 R10)

(2)

Choose the operation to solve the problem. Calculate to find the answer.

Jane made talked on her phone for 38 minutes. Each minute cost her $1.73. How much did she pay to talk for 38 minutes?


(Multiply; $1.73 x 38 =$65.74)

(3)

Identify the pattern being used to increase the number of dots: _______


● ●●●● ●●●●●●●● ●●●●●●●●●●●●●●●●


(multiply by 4)

(4)

Solve the problem with multiple steps.


There was a car wash to raise money for new track uniforms. On Saturday, the team made $172.00 and on Sunday they made $296.00. They had to pay the coach back for the supplies which cost $32.96. How much money did the track team make to raise money for the uniforms?


(First, add $172.00 + $296.00 = $468.00; Next, subtract $468.00 - $32.96 = $435.04)

(5)

Find the probability of the event:

There are 12 marbles in a bag. Five marbles are blue, three marbles are yellow, 2 marbles are red, and 2 marbles are green. What is the probability of choosing a yellow marble? Write in simplest form.


________


(3/12 or ¼ (simplest form)

Learning Tips

(1)

Correcting quotients

The quotient is too large if the product of the quotient and divisor is greater than the dividend.


The quotient is too small if the remainder amount is larger than the divisor.


Math vocabulary:

Quotient- answer for a division problem


Divisor- The number that divides the dividend


Dividend-The number that is to be divided in a division problem


Remainder- The amount left over after you found the answer to the division problem.


i.e.) 627 ÷ 8 = 78 r 3


627 ÷ 8 = 78 r 3 -Quotient

627 ÷ 8 = 78 r 3 -Divisor

627 ÷ 8 = 78 r 3- Dividend

627 ÷ 8 = 78 r 3 - Remainder


How to check your division problem:

__6__r2

5) 32

-30

2

Check: Multiply the quotient and the divisor, then add the remainder. Your answer should equal to the dividend.

i.e.) 6 x 5 = 30 + 2 = 32 (it is correct)


(2)

Review with the child how to determine the accurate operation for word problems by reviewing the clue words to know when to add, subtract, multiply or divide (+, -, x, ÷).

Write out math story problems on index cards and underline the clue words. Have your child determine which operation to use by looking at the clue words.

Addition Clue Words

Subtraction Clue Words

add
sum
total
plus
in all
both
together
increased by
all together

subtract
difference
take away
less than
are not
remain
decreased by
have left
change (money problems)
how much more
fewer



Multiplication Clue Words

Division Clue Words

times
product of
multiplied by
by (dimension)

quotient of
divided by
half for a fraction
as much
split
separated
cut up
parts
sharing something equally

(3)

Practice breaking apart word problems in order to solve multiple steps.

Write a word problem with multiple steps on a sheet of paper. Break apart the problem and write the steps individually on an index card. Have your child determine the order in which the steps need to be solved in order to come up with the final solution (first, second, third). Once the order has been determined, allow them time to solve each part and see if the final solution is correct.

(4)

Make patterns with shapes, colors, etc. and have your child determine which pattern will come next and explain how they came up with that conclusion.

Number Patterns:

Practice skip counting using a number line in order to help your child find patterns in a list of numbers.


When you are using a number line, it will be best to color code the numbers (counting by 2s (place a blue dot above each number).

(5)

Review fractions


Numerator = part

Denominator = whole


Probability: Numerator = choice of outcome

Denominator = total # of possible outcomes


Practice writing fractions using figures: Which part of the figure is shaded (write with fraction)

Marbles In A Bag

Get a color assortment of marbles (red, blue, green, swirls, etc.) and count the number of marbles for each color, then count the total number of marbles. Have your child practice writing the fraction for the part (# of marbles for a color) and whole (total marbles).


Once the numbers have been determined, relate the fractions to probability. The color with the most marbles will have a higher probability of being chosen out of the bag, than the color with the least marbles.


Extra Help Problems

(1)

Correct the quotient: Check if the estimate is too high, too low or accurate and choose the explanation. Calculate to find the accurate answer.

___6_R4

17) 106

- 102

4



(a) The estimate is too high because the product ____ is greater than the dividend.

  1. The estimate is too low because the difference of _____ is greater than the divisor.

  2. The estimate is accurate because the difference is less than the divisor. Correct remainder.


(c)

(2)

Correct the quotient: Check if the estimate is too high, too low or accurate and choose the explanation. Calculate to find the accurate answer.

___9_R5

13) 112

- 117

-5


  1. The estimate is too high because the product (9 x 13 = 117) is greater than the dividend.

  2. The estimate is too low because the difference of (112 – 117 = -5) is greater than the divisor.

  3. The estimate is accurate because the difference is less than the divisor. Correct remainder.


(a- Correct answer is 8 R8)

(3)

Correct the quotient: Check if the estimate is too high, too low or accurate and choose the explanation. Calculate to find the accurate answer.

___4_

14) 123

- 56

67



  1. The estimate is too high because the product (14 x 4 = 56) is greater than the dividend.

  2. The estimate is too low because the difference of (123- 56 = 67) is greater than the divisor.

  3. The estimate is accurate because the difference is less than the divisor. Correct remainder.


(b – Correct answer is 8 R11)

(4)

Correct the quotient: Check if the estimate is too high, too low or just right and choose the explanation. Calculate to find the accurate answer.

___7_

15) 100

- 105

-5



  1. The estimate is too high because the product (15 x 7 = 105) is greater than the dividend.

  2. The estimate is too low because the difference of (100- 105 = -5) is greater than the divisor.

  3. The estimate is accurate because the difference is less than the divisor. Correct remainder.


(a- the correct answer is 6 R10)

(5)

Correct the quotient: Check if the estimate is too high, too low or just right and choose the explanation. Calculate to find the accurate answer.

___8_ R3

20) 163

- 160

3


  1. The estimate is too high because the product (8 x 20 = 160) is greater than the dividend.

  2. The estimate is too low because the difference of (163- 160 = 3) is greater than the divisor.

  3. The estimate is accurate because the difference is less than the divisor. Correct remainder.


(c)

(6)

Choose the operation to solve the problem. Calculate to find the answer.


How many more people enjoy chicken more than hot dogs? ___________

(Subtract; 87- 63 = 55 people)

(7)

Choose the operation to solve the problem. Calculate to find the answer.

Using the graph, how many people enjoy hamburgers, pizza and spaghetti? ___________

(Addition; 40 + 55 + 36 = 131 people)

(8)

Choose the operation to solve the problem. Calculate to find the answer.


The teacher bought 8 pizzas that had 12 slices each. How many slices were there total?


(Multiply; 12 x 8 = 96)

(9)

Choose the operation to solve the problem. Calculate to find the answer.

There are 162 seats in the auditorium. If there are 9 rows. How many seats are in each row? ________


(Divide; 162 ÷ 9 = 18)

(10)

Choose the operation to solve the problem. Calculate to find the answer.


It takes Allison 2 minutes to complete one math problem. How long will it take her to complete 23 math problems? ________


(Multiply; 23 x 2 = 46 minutes)

(11)

Identify the pattern being used:

3, 7, 15, 31…


  1. Multiply by 2; add 1

  2. Multiply by 3

  3. Multiply by 2; subtract 1


(a)

(12)

Identify the pattern being used:

18, 21, 24, 27…


  1. add 3

  2. multiply by 3

  3. add 3; subtract 1


(a)

(13)

Identify the pattern being used:

2:15, 3:00, 3:45. 4:40


  1. time increases by 15 minutes

  2. time increases by 45 minutes

  3. time decreases by one hour


(c)

(14)

Identify the pattern being used:

B, C, D, F, H, J…


(a) skip one letter of the alphabet

(b) write two letters, then skip one

(c) write consonant letters in order


(c)

(15)

Identify the pattern being used:

180, 170, 160, 150, 140…


  1. divide by 10

  2. add 10

  3. subtract 10


(c)

(16)

Solve the problem with multiple steps.

Jesse walks dogs to make extra money. He charges $7.00 to walk each dog. If he walks 8 dogs three times per week. How much money will he make in one week?

______________

(Multiply $7.00 x 8 = $56.00; Then multiply $56.00 x 3 = $168.00 per week)

(17)

Solve the problem with multiple steps.

Jesse walks dogs to make extra money. He charges $7.00 to walk each dog. If he walks 8 dogs three times per week. How much money will he make in one month?

______________


(Multiply $7.00 x 8 = $56.00; Then multiply $56.00 x 3 = $168.00 per week; Multiply $168.00 x 4 = $672.00)


(18)

Solve the problem with multiple steps.


Darcy practices the piano from 4:00 pm to 6:30 pm. She practices 4 times per week. How many hours per week does Darcy practice?

(Calculate how many hours she practices per day = 2 ½ (or 2.5); Multiply 2.5 x 4 = 10 hours)


(19)

Solve the problem with multiple steps.


Darcy practices the piano from 4:00 pm to 6:30 pm. She practices 4 times per week. How many hours per week does Darcy practice? How many hours will she practice until her recital in 6 weeks?


(Calculate how many hours she practices per day = 2 ½ (or 2.5); Multiply 2.5 x 4 = 10 hours; Multiply 10 hours x 6weeks = 60 hours )


(20)

Find the probability of the event (use simplest form). What is the probability of landing on a vowel? ______________

(2/8 or ¼ (simplest form)


(21)

Find the probability of the event (use simplest form). What is the probability of landing on a consonant letter? ___________


(6/8 or ¾ [simplest form])

(22)

Find the probability of the event (use simplest form). What is the probability of landing on an even number? ___________



(4/8 or 1/2 [simplest form])

(23)

Find the probability of the event:

There are 12 marbles in a bag. Five marbles are blue, three marbles are yellow, 2 marbles are red, and 2 marbles are green. Which marbles have the same probability of being chosen? What is the probability?

______________


(green and red marbles; 2/12 or 1/6)

(24)

Find the probability of the event:

What is the probability of getting an 8 if you are tossing a number cube that is labeled 1-6? ______________


(0/6)


(25)

Find the probability of the event:

What is the probability of choosing an odd number on a number cube (die) that is labeled 1-9? ___________________


(5/9)

 

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