WEEK 6-PROBLEMS-WITH-RATIONAL-NUMBERS

Problems with Rational Numbers

Objectives

Start

Review of PEMDAS

Exercises with Exponents

Real-World Problems

Practice Problems

Review of PEMDAS

PEMDAS ( ),()³,x,÷,+,-

FIRST

(), [],

Parenthesis (Kind of)

()²,()³,...

Exponentials (and roots)

Multiplications and Divisions

x, ÷

Additions and substractions

+,-

LAST

Let's see some examples:

Example 1: Solve

To solve multi-step problems, remember the order of operations:

Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right).

Try it by yourself:

Exercises with Exponents

Let's see some examples:

Example 2: Solve

Example 1: Find the value of

Real-World Problems

Bakery Resources and Budgeting

John is opening a bakery where he requires 2×10³ kg of flour. Looking up on internet, one kg of flour costs $4.50, and delivery cost is $200. How much does all flour cost?

a) Read the problem, identify context, givens in the situation and question. b) Draw the situation and put givens on them. c)How much does all flour cost?

Solution

Area of a Terrain

The area of a land is a trapezoid with measures shown in the figure as follows:

We are interested in finding the area of the land.

a) Read the problem and identify context, givens and question in the situation. b) Find the area of the land.

Solution

Practice Problems

Try it by Yourself

You go to the supermarket and see a package of 6 apples at $8200 COP. Additionally you go there using public transportation at cost of $6000 COP.

Find the cost of each apple including transportation costs. In order to do that: a) Place the givens and question in a drawing. b) Make a solution plan.

🤔

07:00

Try it by Yourself

Melissa wants to paint the front area of her house with the measurements shown in the following figure:

a) Write the context and the givens of the situation. b) Find the total area to paint. Plan your strategy of solution.

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07:00

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

8TH-PROBLEMS-WITH-RATIONAL-NUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MATERIAL

It is highly advised to have:

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

Solution

Answer

Step 1

Step 3

Step 2

Step 5

Step 4

b) Land Area: 2.2×10⁵ m²

a)

b)

Context: A land (terrain) with an irregular shape composed of a square and a triangle

Step 3

Step 1

Step 4

Step 2

Solution

Answer

Step 1

Step 3

Step 2

Step 5

Step 4

b) Land Area: 2.2×10⁵ m²

a)

b)

Context: The front of a house to be painted and where is required the area.

Step 3

Step 1

Step 4

Step 2

Solution

Answer

Step 1

Step 3

Step 2

Step 5

Step 4

a) Price of each apple: $2400

a)

b)

Step 1

🍎 🍎🍎 🍎 🍎 🍎

🚌

Step 2

Step 3

Step 4

$8200

$6000

Step 5

price🍎 ?

MA.8.NSO.1 Solve problems involving rational numbers, including numbers in scientific notation, and extend the understanding of rational numbers to irrational numbers. MA.8.NSO.1.7 Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.

Solution

Answer

Step 1

Step 3

Step 2

Step 5

Step 4

c) The total cost of flour is $9200.

a)

b)

🚚

Step 3

Context: John will open a new bakery (for bread) and requires flour.

Step 1

$4.50 per kg

$200 delivery

Flour=2×10³ kg Cost?

Step 2

c)

Step 4

Cost= Price per kg × total kg+ delivery cost

Step 5