# 6th Grade - Calculate By Hand Or Using A Calculator

 Grade Level: 6th Skill: Algebra Topic: Calculate by Hand or Using a Calculator Goal: Solve problems manually by using the correct order of operations or by using a scientific calculator. Skill Description: Follow the order of operations rules to solve problems with multiple operations, showing the step-by-step process. Use the order of operations, together with a scientific calculator, to solve expressions with more than one operation.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Evaluate the expression. 25/(4 + 1) – 3 (122) (2) (6 + 18) 23 (32) (3) 56(11) – (14 – 2 x 2) (606) (4) (175 – 5) x 52 2 (2,125) (5) [(4 + 5) x (15 ÷ 5) – 7 + 125] x 72 (7,105)

### Learning Tips

(1)

It is crucial that children memorize order of operations. They will need to use them throughout sixth grade and beyond. It is imperative that children follow these rules every time he/she solves and expression with more than one operation. Often times, the order of operations are taught using the phrase, “please excuse my dear aunt sally”, where the p stands for parentheses, e = exponents, m = multiply, d = divide, a = add, and s = subtract. The problem with this teaching strategy is that it does not teach students to move from the left side of the problem to the right using multiply and divide are interchangeably, as well as add and subtract. So, if solving a problem such as 8/4 x 2. Many students will multiply first, when he/she really needs to divide. A more appropriate way to teach would be to use a chant with hand movements to aid in memorization. Here’s an example (the words in italics are chanted aloud, the regular type is an example of the concept and bolded words are hand signals):

Grouping Symbols”

(2+4), [(3 x 4) + 5 ]

Child holds up both hands in a “c” shape to represent parentheses

Exponents

42

Child holds up two fingers with hand above head to show exponents (ex. a number squared)

Mulitply or divide, divide or multiply left to right”

3x4†2 or 8/4•5

Child crosses arms in an X shape for multiply, uses the left arm to show the division slash / and points from left to right.

2 + 4 – 6 or 9 - 6 + 11

Child crosses arms in a + shape for add, uses right arm to show a minus sign – and points left to right.

(2)

Many children may feel overwhelmed by expressions with more than one operation. This is why it’s important for children to isolate the part of the problem that he/she is solving. One way to do this is to use boxes and color-coding. Here’s an example of this process.

9 (4+7) -5

9 x 11 – 5

9 x 11 – 5

99 – 5

99 – 5

94

Sticky notes can also be used to block out parts of the problem that are not being worked on.

(3)

Organization is the key to success in solving expressions using the order of operations. One way to stay organized is to create a PEMDAS table that can be checked off as operations are performed or determined not to be a part of the problem. (PEMDAS stands for: p = parentheses, e = exponents, m = multiply, d = divide, a = add, and s = subtraction). However, make sure that you remember that the M does not always come before the D. M and D are equal partners. Whichever operation is on the left side of the operation is the one that must be solved first. The same goes for A and S. For these reasons, our PEMDAS table is set up differently than others you may find in teacher’s manuals or online. Here’s a sample table.

 P E M, D or D, M A, S or S, A

(4)

A scientific calculator can be used to check manually written answers. However, it is important that children be taught the proper use of the scientific calculator. It is important to find the meaning of each function key. These can be different for each brand of calculator, so be sure to research yours.

(5)

Children will be asked to use the order of operations for many different math concepts. For example, some expressions may require children to use the rules for computing integers, fractions and the order of operations. It is important that your child work slowly and think about all concepts involved when solving these challenging concepts. Remind your child that order is crucial. For, you will get two different answers if you don’t follow the correct order. Model this using the following example or one of your own.

8 + 10/2

Correct Order Incorrect Order

10/2 = 5 8 + 10 = 18

8 + 5 18/2

### Online Resources

 (1) (2) (3)

### Extra Help Problems

 (1) 5 + 14/7 (7) (2) 8 x 9 – 4 + 11 (79) (3) (2 + 13)/3 x 10 (50) (4) (14 + 15) – (11 + 4) (15) (5) (5 + 9) 43 (896) (6) 290/10 + 7 • 2 (43) (7) 16(12) – (20 - 4 x 5) (192) (8) 49 + 1 – 5 x 6 + 26 (46) (9) 175 – 5 x 42÷2 (135) (10) 25 + 12 x 11 – 14 (143) (11) (102+ 96) x (192 ÷ 12) (3,168) (12) (18 + 2 x 6) – 32 (21) (13) (22 – 6 + 15) x 2 (102 ÷ 2 x 3) (9,486) (14) [(4 + 16) x (20 ÷ 5) – 12 + 125] x 52 (4,825) (15) 150 – 5 x 22 10 (58) (16) -5 + -56  4 (-19) (17) (-100+ 96) x (-192 ÷ -12) (-64) (18) (6 + 18) -23 (-192) (19) -9/3 + 7 • -4 (-31) (20) (2.56 – 1.4) x 3.4 (3.944) (21) 9.5 - 1.24 + 3.426 x 7 (32.242) (22) 9.2 x 1.35 2 (6.21) (23) 1/5 + 3/10 x 4/5 (11/25) (24) (3/4 – ½) x 6 + 2 ½ (4) (25) (-16 x ¾) + (-11.5 x 16.2) (-198.3)