# 4th Grade - Make And Check Precise Calculations

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

## Building Blocks/Prerequisites

### 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 The estimate is too high because the product 90 is greater than the dividend. The estimate is too low because the difference of (136 – 90 = 46) is greater than the divisor. 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 addsumtotalplusin allbothtogetherincreased byall together subtractdifferencetake awayless thanare notremaindecreased byhave leftchange (money problems)how much morefewer Multiplication Clue Words Division Clue Words timesproduct ofmultiplied byby (dimension) quotient ofdivided byhalf for a fractionas muchsplitseparatedcut uppartssharing 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.