Unit 1: Whole Number Foundations

Unit 1 Resources & Lessons

Use the buttons below to access unit-wide resources or jump to a specific lesson.

Daily Lesson Slides

Day 1: Place Value

Day 2: Estimation

Day 3: Fact Families

Day 4: Order of Operations

Day 5: Multiplication & Division Basics

Extra Practice: Multiplication & Division Tips

Unit 1 Quiz Study Guide

Day 1: What Numbers Really Mean (Place Value)

Objective: To write and understand numbers in standard, expanded, and word form.

I Do: The Concept Explained

The most important idea in math is that a digit's position (where it is) changes its value (what it's worth). A '7' can mean 7, 70, or even 7,000,000 depending on its place. Let's look at the number 345.

Hundreds
Tens
Ones
3
4
5

Even though you see a 3, a 4, and a 5, their values are different because of their place:

  • The 3 is in the Hundreds place, so its value is really 300.
  • The 4 is in the Tens place, so its value is really 40.
  • The 5 is in the Ones place, so its value is just 5.

Here is how we write this number in three different forms:

1. Standard Form: This is the normal way we write numbers.

345

2. Expanded Form: This means "stretching out" the number to show the true value of each digit as an addition problem.

\(300 + 40 + 5\)

3. Word Form: This is how you would say the number out loud. Remember to use a hyphen for numbers between 21 and 99 (like forty-five).

Three hundred forty-five

We Do: Check Your Understanding

Fill in the blanks to show you understand the key ideas.

1. In the number 7,462, the digit 4 has a value of
2. The position of a digit determines its

You Do: Practice Problems

Write the number 3,091 in the forms below.

Expanded Form:
Word Form:

You Do More: Extra Practice

Consider the number 52,607.

What is the value of the 2?
Write in Expanded Form:
Write in Word Form:

Notes & Practice

Fill in the blanks and solve the problems.

1. In the number 7,462, the digit 4 has a value of .

2. The position of a digit determines its .

Practice: Write the number 3,091 in the forms below.

Expanded Form:

Word Form:

Extra Practice: Consider the number 52,607.

What is the value of the 2?

Expanded Form:

Word Form:

Day 2: Addition, Subtraction & Estimation

Objective: To use rounding to estimate answers before calculating.

I Do: The Concept Explained

Estimation is a way to make a quick, smart guess before you do the exact math. It helps you know if your final answer is reasonable. The main tool for estimation is rounding.

How to Round: Look at the digit to the right of the place you're rounding to. If that digit is 5 or more, round up. If it's 4 or less, keep the digit the same (round down). All digits to the right become zeros.

Example Problem: You have $48 and spend $29 on a game. About how much money do you have left?

Step 1: Estimate. We round the numbers to the nearest ten to make them "friendlier."
  • $48 is close to $50 (the 8 tells us to round up).
  • $29 is close to $30 (the 9 tells us to round up).

Now, do the easy math: \($50 - $30 = $20\). Our smart guess is that we'll have about $20 left.

Step 2: Calculate. Now we find the exact answer.

\($48 - $29 = $19\)

Step 3: Compare. Is our exact answer ($19) close to our estimate ($20)?

Yes, it is! This tells us our calculation is very likely correct. Estimation is a great way to catch simple mistakes.

We Do: Check Your Understanding

1. To estimate, you first the numbers to make them friendly.
2. The final step is to your exact answer and your estimate.

You Do: Practice Problems

You buy items costing $9.95 and $4.25. First, estimate the total by rounding to the nearest dollar. Then, find the exact total.

Estimated Total: $
Exact Total: $

You Do More: Extra Practice

A school library has 847 fiction books and 582 non-fiction books. First, estimate the total number of books by rounding to the nearest hundred. Then, find the exact total.

Estimated Total Books:
Exact Total Books:

Notes & Practice

1. To estimate, you first the numbers to make them friendly.

2. The final step is to your exact answer and your estimate.

Practice: You buy items costing $9.95 and $4.25. First, estimate the total by rounding to the nearest dollar. Then, find the exact total.

Estimated Total: $

Exact Total: $

Extra Practice: A school library has 847 fiction books and 582 non-fiction books. First, estimate the total number of books by rounding to the nearest hundred. Then, find the exact total.

Estimated Total Books:

Exact Total Books:

Day 3: Multiplication & Division Fact Families

Objective: To understand the inverse relationship between multiplication and division.

I Do: The Concept Explained

Multiplication and division are inverse operations. This is a fancy way of saying they are opposites—they undo each other. A Fact Family is a group of four math facts that use the same three numbers. If you know one fact, you can figure out the other three!

Let's use the simple numbers 2, 5, and 10.

Example: Let's start with the multiplication fact \(2 \times 5 = 10\).

Fact 1 (Multiplication): \(2 \times 5 = 10\)

This means "2 groups of 5 equals 10."

Fact 2 (Multiplication): \(5 \times 2 = 10\)

You can flip the first two numbers (this is the Commutative Property) and the answer is the same. "5 groups of 2 also equals 10."

Fact 3 (Division): \(10 \div 2 = 5\)

Division starts with the biggest number (the product). "If you take 10 and split it into 2 equal groups, there will be 5 in each group."

Fact 4 (Division): \(10 \div 5 = 2\)

"If you take 10 and split it into 5 equal groups, there will be 2 in each group."

We Do: Check Your Understanding

1. Multiplication and Division are called operations.

You Do: Practice Problems

Given the fact \(6 \times 8 = 48\), write the other three facts in its family.

Fact 2:
Fact 3:
Fact 4:

You Do More: Extra Practice

The numbers 7, 9, and 63 form a fact family. Write all four facts.

Fact 1 (Mult):
Fact 2 (Mult):
Fact 3 (Div):
Fact 4 (Div):

Notes & Practice

1. Multiplication and Division are called operations.

Practice: Given the fact \(6 \times 8 = 48\), write the other three facts in its family.

Fact 2:

Fact 3:

Fact 4:

Extra Practice: The numbers 7, 9, and 63 form a fact family. Write all four facts.

Fact 1:

Fact 2:

Fact 3:

Fact 4:

Day 4: Order of Operations (PEMDAS)

Objective: To apply the order of operations to solve problems with multiple steps.

I Do: The Concept Explained

Think of PEMDAS as the "rules of the road" for math. To make sure everyone gets the same answer for a problem like \(5 + 2 \times 3\), we have to do the operations in a specific order. A good way to remember it is: Please Excuse My Dear Aunt Sally.

P: Parentheses ( ). Anything inside parentheses is a VIP group that you must solve first.
E: Exponents. (We'll learn more about these later).
M/D: Multiplication (\(\times\)) and Division (\(\div\)). These are partners. You solve them as you see them from left to right. Don't always do multiplication first!
A/S: Addition (+) and Subtraction (-). These are also partners, and you solve them last, from left to right.

Example Problem: Solve \(5 + (2 \times 3)\)

Step 1: P (Parentheses). We have them! We must do the math inside the parentheses first.

\(2 \times 3 = 6\)

Now, we rewrite our problem with this new, simpler piece: \(5 + 6\)

Step 2: E (Exponents). None.

Step 3: M/D (Multiplication/Division). None left.

Step 4: A/S (Addition/Subtraction). We have addition!

\(5 + 6 = 11\)

The final answer is 11.

We Do: Check Your Understanding

1. In PEMDAS, Multiplication and are partners done from left to right.

You Do: Practice Problems

Solve the following expression step-by-step.

\(20 - (3+1) \times 4\)
Step 1 (Parentheses):
Step 2 (Multiplication):
Final Answer:

You Do More: Extra Practice

Solve this problem, remembering the left-to-right rule for M/D.

\(10 \div 2 + 3 \times 5\)
Step 1 (Division):
Step 2 (Multiplication):
Final Answer:

Notes & Practice

1. In PEMDAS, Multiplication and are partners done from left to right.

Practice: Solve the following expression step-by-step.

\(20 - (3+1) \times 4\)

Step 1 (Parentheses):

Step 2 (Multiplication):

Final Answer:

Extra Practice: Solve the following expression step-by-step.

\(10 \div 2 + 3 \times 5\)

Step 1 (Division):

Step 2 (Multiplication):

Final Answer:

Day 5: Multiplication Tables & The Basics

Objective: To build fluency with multiplication facts and understand the core concepts of multiplication and division.

I Do: The Concept Explained

What is Multiplication? It's just a fast way of adding. For example, \(3 \times 4\) is the same as adding 4, three times: \(4 + 4 + 4 = 12\). The numbers you multiply are called factors, and the answer is the product.

3 (factor) × 4 (factor) = 12 (product)

What is Division? It's the opposite (or inverse) of multiplication. It means splitting a number into equal groups. For example, \(12 \div 4 = 3\) asks, "If you have 12 items and split them into 4 equal groups, how many items are in each group?" The answer is 3.

12 (dividend) ÷ 4 (divisor) = 3 (quotient)

We Do: Check Your Understanding

1. Multiplication is a shortcut for repeated
2. The answer to a multiplication problem is the
3. The answer to a division problem is the

You Do: Practice Problems

Use your multiplication knowledge to solve these!

\(6 \times 7 =\)
\(9 \times 5 =\)
\(24 \div 8 =\)
\(49 \div 7 =\)

You Do More: Extra Practice

Solve the problem below.

If there are 8 spiders and each spider has 8 legs, how many legs are there in total?

Notes & Practice

1. Multiplication is a shortcut for repeated .

2. The answer to a multiplication problem is the .

3. The answer to a division problem is the .

Practice Problems:

\(6 \times 7 = \)

\(9 \times 5 = \)

\(24 \div 8 = \)

\(49 \div 7 = \)

Word Problem:

If there are 8 spiders and each spider has 8 legs, how many legs are there in total?

Ready to test your knowledge?

You have completed the notes for Unit 1. Click the button below to take the quiz.

Take the Unit 1 Quiz