Operations and Algebraic Thinking – Sum

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 a school activity. 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