Grade 3
  1. Number Sense and Numeration  1.1. Understanding Numbers  1.1.1. Reading and Writing Numbers up to 10,000  1.1.2. Place Value up to Thousands  1.1.3. Comparing and Ordering Numbers  1.1.4. Rounding Numbers to the Nearest Ten and Hundred  1.1.5. Skip Counting by 2s, 5s, 10s, and 100s up to 1,000  1.2. Operations with Whole Numbers  1.2.1. Addition and Subtraction up to 1,000  1.2.2. Multiplication Facts (up to 10 x 10)  1.2.3. Division Facts (up to 100)  1.2.4. Multiplication as Repeated Addition  1.2.5. Division as Equal Sharing  1.2.6. Word Problems with Addition, Subtraction, Multiplication, and Division  1.3. Estimation  1.3.1. Estimating Sums and Differences  1.3.2. Estimating Products and Quotients  1.4. Understanding Even and Odd Numbers
  2. Fractions and Decimals  2.1. Understanding Fractions  2.1.1. Identifying and Representing Fractions  2.1.2. Fractions of a Whole and Part of a Set  2.1.3. Comparing and Ordering Fractions with Like Denominators  2.1.4. Equivalent Fractions  2.1.5. Simple Fraction Word Problems  2.2. Introduction to Decimals  2.2.1. Tenths and Hundredths as Decimals  2.2.2. Relationship between Fractions and Decimals
  3. Measurement  3.1. Length  3.1.1. Measuring in Centimeters and Meters  3.1.2. Comparing and Ordering Lengths  3.1.3. Estimating Lengths  3.1.4. Converting Between Centimeters and Meters  3.2. Mass  3.2.1. Measuring in Grams and Kilograms  3.2.2. Estimating and Comparing Mass  3.3. Capacity  3.3.1. Measuring in Milliliters and Liters  3.3.2. Estimating and Comparing Capacity  3.4. Time  3.4.1. Telling Time to the Nearest Minute  3.4.2. Calculating Elapsed Time  3.4.3. Using a Calendar  3.4.4. Understanding A.M. and P.M.  3.5. Area and Perimeter  3.5.1. Calculating Perimeter of Simple Shapes  3.5.2. Estimating and Measuring Area of Shapes  3.5.3. Finding Area by Counting Squares
  4. Geometry  4.1. Properties of Shapes  4.1.1. Identifying 2D Shapes (Triangles, Quadrilaterals, Circles, etc.)  4.1.2. Identifying 3D Shapes (Cubes, Spheres, Cylinders, etc.)  4.1.3. Describing Attributes of 2D and 3D Shapes  4.1.4. Recognizing Parallel and Perpendicular Lines  4.2. Symmetry and Transformations  4.2.1. Recognizing Lines of Symmetry  4.2.2. Identifying Flips, Slides, and Turns  4.3. Angles  4.3.1. Understanding Right Angles  4.3.2. Comparing Angles (Acute, Right, Obtuse)
  5. Data Management and Probability  5.1. Data Collection and Organization  5.1.1. Collecting Data using Surveys and Experiments  5.1.2. Organizing Data using Tally Charts and Tables  5.2.1. Creating and Interpreting Pictographs  5.2.2. Creating and Interpreting Bar Graphs  5.2.3. Reading Simple Line Graphs  5.3. Probability  5.3.1. Understanding Basic Probability Terms (Certain, Possible, Impossible)  5.3.2. Predicting Outcomes  5.3.3. Simple Probability Experiments
  6. Patterns and Algebra  6.1. Patterns  6.1.1. Identifying and Extending Numeric Patterns  6.1.2. Identifying and Extending Shape Patterns  6.1.3. Creating Patterns Using Rules  6.2. Introduction to Algebra  6.2.1. Understanding Variables as Unknowns  6.2.2. Solving Simple Addition and Subtraction Equations  6.2.3. Using Patterns to Solve Problems
  7. Problem-Solving Skills  7.1. Strategies for Problem-Solving  7.1.1. Using Pictures or Diagrams  7.1.2. Identifying Patterns in Problems  7.1.3. Making Organized Lists  7.1.4. Guessing and Checking  7.1.5. Using Logical Reasoning  7.1.6. Breaking Down Problems into Steps

Grade 3 → Number Sense and Numeration → Estimation ↓


Estimating Sums and Differences


Estimating is like a magical tool that helps us make quick decisions and solve problems in our daily lives, without needing to know the exact answer. Imagine you are at a store, and you want to buy a candy, a toy, and a book, but you only have $10. Estimating helps you quickly estimate if these items are within your budget. In 3rd grade math, we focus on estimating sums (adding numbers) and differences (subtracting numbers). This is an essential skill because it helps you understand numbers better and make decisions faster.

Why is assessment important?

Assessment is important because:

  • This saves time.
  • This is helpful when you need an answer right away.
  • This improves your number sense.
  • This is a skill you will use for the rest of your life.

What is the estimated amount?

Estimating a sum means finding an approximate total when you add two or more numbers. Instead of calculating the exact number, you estimate a number that's pretty close. Let's see how this works with an example:

Suppose you have the numbers 27 and 34. When you add them exactly, you get:

27 + 34 = 61

However, if you want an approximate amount, you can round each number to the nearest ten and then add them up:

Round 27 to 30, and 34 to 30.
30 + 30 = 60

The estimated total is 60, which is close to the actual total of 61.

What is estimating the difference?

Estimating the difference involves getting an approximate result when subtracting one number from another. Let's work on this:

Suppose you want to subtract 19 from 48. The exact subtraction will look like this:

48 - 19 = 29

For the approximate difference, first round the numbers to the nearest ten, then subtract them:

Round 48 to 50, and 19 to 20.
50 - 20 = 30

The estimated difference is 30, which is close to the actual difference of 29.

Rounding off numbers

To estimate the sum and difference, we start by rounding the numbers. Rounding helps simplify numbers, making them easier to work with. Here's a quick guide on how to round numbers:

  • Look at the digit to the right of the place value you want to round off.
  • If the score is 5 or more then round it up.
  • If the score is less than 5, round it down.

Let's practice rounding some numbers:

Round 76 to the nearest tens:

76 -> 80 (since 6 is more than 5, round up)

Round 32 to the nearest tens:

32 -> 30 (since 2 is less than 5, round down)

Steps to estimate the sum and difference

Now, let us understand the steps to estimate the sum and difference:

Step 1: Round off the numbers

Start by rounding each number to the nearest ten or another place value, depending on what size number you're working with.

Step 2: Add or subtract rounded numbers

Perform addition or subtraction using rounded numbers.

Step 3: Check your guess

Compare your estimate to the actual sum or difference. This will help you understand how accurate your estimate is. With practice, your estimation will get better!

Visual example: guessing the amount

Let's see what this process looks like with a visual example of estimating the sum of 47 and 68.

4768

1. Rounds 47 to 50.
2. Rounds 68 to 70.
3. Add rounded numbers:

50 + 70 = 120

Visual example: estimating the difference

Now, we will give a visual example of estimating the difference between 85 and 53.

8553

1. Round off 85 to 90.
2. Round off 53 to 50.
3. Subtract rounded numbers:

90 - 50 = 40

Assessment in everyday life

You may be wondering when you would use an estimate. In fact, estimates are used in everyday life:

  • At the store: To quickly estimate the total cost of the items in your cart.
  • On the go: To estimate the total time it will take to reach your destination.
  • At restaurants: To estimate how much you should tip.
  • At school: When you need to quickly check if your answer in math class is correct.

Activity: Practice with estimation

Let's do a quick exercise to check your understanding:

Find the sum of 24 and 39.

Step 1: Round each number to the nearest ten.
Hint: Raise 24 to 20, and raise 39 to 40.

Step 2: Add the rounded numbers.

20 + 40 = 60

The estimated amount is 60.

Now estimate the difference between 92 and 46.

Step 1: Round each number to the nearest ten.
Hint: Round 92 to 90, and round 46 to 50.

Step 2: Subtract the rounded numbers.

90 - 50 = 40

The estimated difference is 40.

Tips and tricks for better estimation

  • Practice rounding numbers often as this is the key to quick estimation.
  • While rounding, remember that half numbers like 45 can be rounded up or down as per your convenience.
  • Use estimation as a tool to check whether your answer to a math problem is reasonable.
  • Keep in mind that guessing does not give an exact answer, but rather a very close estimate.

Conclusion

Estimating sums and differences is a valuable skill that enhances mental math abilities, encourages logical thinking, and saves time. By practicing estimating, you gain confidence in handling numbers and make better decisions. Remember, estimating is not about getting the right answer, but about finding an answer that is close enough to help you make decisions efficiently. Keep practicing, and you'll see how powerful estimating can be in your everyday life!


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Estimating Sums and Differences

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