What is a Sum?
Definition: A sum is the total you get when combining two or more numbers or quantities through addition.
Key Features of Sums:
- Represents the idea of “putting together” or “adding to”
- Written using the plus sign (+)
- The = sign shows the total result
How to Find a Sum
Step-by-Step Process
1. Determine what numbers are being added
2. Collect all the numbers (or calculate in your mind/through your own method).
3. Add the numbers you collected to determine the total.
4. Describe the total in the addition sentence (note: the sentence does not have to be a complete sentence).
In this example,
🍎🍎 + 🍎🍎🍎 = 🍎🍎🍎🍎🍎
“Two apples are added to three apples to get five apples.”
→ 2 + 3 = 5
Real-Life Sum Scenarios
Example 1: Car Collection
* 4 car were in your car collection. The cars were originally cars
* 2 cars were donated from a friend to your car collection.
* 6 total cars will now be in your car collection (4 original plus 2 donor) = 6 cars total.
Classroom Pen or Pencil Inventory Example 2 – A classroom has its own set amount of pens or pencils.
In this instance, 5 pens or pencils were checked into the classroom. They were originally checked out and used by a student.
A teacher then donated 3 pens or pencils to the classroom.
So, the classroom now has 8 pens or pencils checked into its inventory (5 + 3 = 8 total pens/pencils).
Cookie Comparison Example 3 – There are 2 plates. Plate A has 6 cookies on it, while Plate B has 4 cookies on it. The total number of cookies on the 2 plates is equal to 10 (6 + 4 = 10 total).
Interactive Practice
Exercise 1: Visual Steps
Consider this equation: 🐶🐶 + 🐶🐶🐶 = (2 + 3 = 5)
Exercise 2: Calculation Using Words
In this exercise, we begin with 7 marbles that we get from winning in a game. And then we get 5 more marbles. Find out how many marbles that makes altogether.
Write down the equation: 7 marbles + 5 marbles = ______
(Correct Answer: 12 marbles)
Exercise 3: Find The Missing Addend
This problem gives you two 🌼’s, and it asks how many additional 🌼’s are missing in order to make a total of 5 🌼🌼’s.
The solution is ____ 🌼’s (3 more).
Tools to Find Sums
| Method | How It Works | Example |
|---|---|---|
| Counting Objects | Use physical items (blocks, toys) | 2 buttons + 3 buttons = 5 |
| Number Line | Hop forward to add numbers | Start at 4, jump 3 → 7 |
| Ten-Frames | Fill grids to visualize 10s | 6 + 4 fills one frame |
Difference
In informal terms, a difference is how many more (or fewer) units of one number are compared to another number.
Difference key characteristics include:
* The idea of taking away and comparing
* The use of the “–” sign when calculating the difference
* An answer shown with the “=”, representing the determined overall value remaining after taking away a number from another number.
Finding a Difference
1. Start with the whole (minuend)
2. Subtract by the second number (subtrahend)
3. Count the remaining amount (difference)
4. Write a subtraction equation
An example of this: 🍎🍎🍎🍎🍎 – 🍎🍎 = 🍎🍎🍎 “5 apples – 2 apples = 3 apples.” So 5 – 2 = 3
Example 1: Toy Cars
7 toy cars 🚗🚗🚗🚗🚗🚗🚗 and I gave 3 to my friend 🚗🚗🚗. So how many do I have? 7 – 3 = 4.
Example 2: Classroom Pencils
10 pencils ✏️✏️✏️✏️✏️✏️✏️✏️✏️✏️ and I broke 4 of them ✏️✏️✏️✏️. So how many do I have? 10 – 4 = 6.
Example 3: Jar of Cookies
There were 8 cookies in our jar 🍪🍪🍪🍪🍪🍪🍪🍪 and I ate 2 of them 🍪🍪. So how many were left? 8 – 2 = 6.
Tools to Find Differences
| Method | How It Works | Example |
|---|---|---|
| Counting Objects | Take away items physically | 6 blocks – 2 blocks = 4 |
| Number Line | Hop backward to subtract | Start at 9, jump back 4 → 5 |
| Ten-Frames | Remove counters to see what’s left | 8 – 3 leaves 5 |
Exercises
