Solve multi-step problems involving multiple operations. |...

SECTION 1

Historical Context & Motivation

Long ago, people like ancient Egyptians solved math problems with many steps to build pyramids. They needed rules to get the right answers every time. Today, multi-step problems help us do the same in school and real life. Without clear steps, answers get mixed up like a jumbled puzzle.

3000 BC

Ancient Math

Egyptians used multi-step calculations for building.

1600s

Order Rules

Math experts created rules like PEMDAS for steps.

1900s

School Standard

Multi-step problems became key in tests like SSAT.

Today

Your Turn

You solve them to ace entrance exams!

These steps fix confusion in tough problems. You can master them too!

SECTION 2

Core Principles

Multi-step problems mix addition, subtraction, multiplication, and division. The key is order of operations, often called PEMDAS. It stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Parentheses First

Do inside () before anything else, like opening a gift first.

Exponents Next

Powers like 2² = 4 come after parentheses.

Multiply/Divide Left to Right

× and ÷ go before + and −.

Add/Subtract Last

Finish with + and − from left to right.

🎮 Game Level Analogy

Think of PEMDAS like game levels. Finish level 1 (parentheses) before level 2 (exponents). Skip steps and you lose!

SECTION 3

Visual Explanation

Follow the arrows from top to bottom. Each box shows the next step in order.

This diagram shows the flow like a roadmap. Start at the top and move down. It keeps your math straight!

SECTION 4

Mathematical Framework

Use PEMDAS every time. Write steps clearly. Check work by plugging back in.

ORDER OF OPERATIONS

PEMDAS: P → E → MD → AS

P = Parentheses, E = Exponents, MD = Multiplication & Division (left to right), AS = Addition & Subtraction (left to right)

EXAMPLE STEP-BY-STEP

(2 + 3) × 4 − 1²

1. (5) × 4 − 1 = 20 − 1 = 19

Always show your work. It builds confidence for SSAT questions.

SECTION 5

Detailed Breakdown of Problem Types

Arrows show steps: subtract first, then multiply and add. Visualizes a word problem.

Word problems mix operations. Draw pictures like this to see steps clearly. Practice makes it fun!

SECTION 6

Worked Example

Solve: 15 − 2 × 3 + 4 ÷ 2

Step 1: Multiplication ×Do 2 × 3 = 6 first.

15 − 6 + 4 ÷ 2

Step 2: Division ÷Next, 4 ÷ 2 = 2.

15 − 6 + 2

Step 3: Subtraction −15 − 6 = 9.

9 + 2

Step 4: Addition +9 + 2 = 11.

See how each step changes the problem? You got this!

SECTION 7

Common Mistakes & How to Avoid Them

Mistake	Why Wrong	Fix It
Doing + before ×	Ignores PEMDAS order.	Check PEMDAS list first.
Forgetting parentheses	Changes the whole answer.	Circle () and do them first.
Wrong left-to-right	Mixes ÷ and × order.	Go left to right always.

✦ KEY TAKEAWAY

Avoid pitfalls like skipping steps in a race. Slow down, follow PEMDAS, and win!

SECTION 8

Connection to Algebra

Arithmetic Multi-Step	Algebra Version
2 + 3 × 4 = 14	2 + 3x = 14, solve for x
Numbers only	Variables like x, y
Follow PEMDAS	Same rules, more steps

Master this now for easier algebra later. You're building a strong math foundation!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

In 5 + 2 × 3, what operation first? A. Add 5 + 2 B. Multiply 2 × 3 C. Subtract 5 − 2 D. Divide 5 ÷ 2 E. Add 2 + 3

PROBLEM 2 — BASIC CALCULATION

What is (4 + 6) ÷ 2? A. 6 B. 10 C. 5 D. 2 E. 20

PROBLEM 3 — INTERMEDIATE

12 ÷ 3 × 2 + 1 = A. 9 B. 17 C. 8 D. 1 E. 24

PROBLEM 4 — APPLIED

Mia has 10 candies. She eats 2 × 3, then gets 5 more. Total? A. 11 B. 19 C. 1 D. 15 E. 21

PROBLEM 5 — CRITICAL THINKING

Store: 25% off 40 shirt is 30, plus 8% tax. Total? A. 32.40 B. 46.80 C. 12 D. 48 E. 34.80

SUMMARY

Lesson Summary

Master multi-step problems with PEMDAS. Do parentheses, exponents, then ×/÷ left to right, +/− last.

Practice steps like game levels. You're ready for SSAT success—keep going!