Math Foundations Unit 1: Whole Number Foundations

Essential Question for the Unit:

"How do the basic rules of numbers help us solve problems accurately and efficiently?"

Weekly Pacing at a Glance

  • Day 1: Place Value & Number Forms (Standard, Expanded, Word).
  • Day 2: Rounding to Estimate Sums and Differences.
  • Day 3: Multiplication & Division Fact Families.
  • Day 4: Order of Operations (PEMDAS).

1. Place Value & Number Forms

The position of a digit determines its value. We can write numbers in several ways.

Form Description Example for 452
Standard Form The normal way to write a number. 452
Expanded Form "Stretching out" the number by the value of each digit. 400 + 50 + 2
Word Form Writing the number out in words. Four hundred fifty-two

2. Estimation with Rounding

To make a smart guess (estimate), we round numbers to make them "friendlier" before calculating.

The 3 Steps of Estimation

  1. Estimate: Round the numbers first, then do the math.
  2. Calculate: Find the exact answer.
  3. Compare: Check if your exact answer is close to your estimate.

Worked Example:

Estimate the sum of 192 + 89.

  • Estimate: Round 192 to 190. Round 89 to 90.
  • Add the rounded numbers: 190 + 90 = 280.
  • Calculate Exact: 192 + 89 = 281.
  • Compare: Our estimate of 280 is very close to the exact answer of 281!

3. Fact Families & Inverse Operations

Multiplication and Division are inverses (opposites). A fact family shows how three numbers are related.

Operation Type Fact Explanation
Multiplication 7 x 8 = 56 7 groups of 8 equals 56.
Multiplication 8 x 7 = 56 You can flip the numbers.
Division 56 ÷ 7 = 8 Start with the total and split it.
Division 56 ÷ 8 = 7 Split it the other way.

4. Order of Operations (PEMDAS)

The rules we follow to solve problems with multiple steps. Think of it as "power levels."

  • Level 1 (Highest Power): Parentheses ( )
  • Level 2: Multiplication (x) and Division (÷) - from left to right.
  • Level 3 (Lowest Power): Addition (+) and Subtraction (-) - from left to right.

Worked Example:

Evaluate 10 - 2 x 3.

  • Multiplication First: 2 x 3 = 6.
  • Rewrite the problem: 10 - 6.
  • Then Subtract: 10 - 6 = 4.
  • Final Answer: 4.

Key Vocabulary

  • Place Value: A digit's position determines its worth.
  • Value: How much a digit is worth.
  • Standard Form: A number written normally (e.g., 123).
  • Expanded Form: A number "stretched out" (e.g., 100+20+3).
  • Word Form: A number written in words.
  • Rounding: Changing a number to a simpler, close number.
  • Estimation: Making a smart guess by rounding first.
  • Fact Family: 4 related facts using 3 numbers.
  • Inverse Operations: Opposites that undo each other.
  • Order of Operations: The rules for solving math problems (PEMDAS).