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 → Problem-Solving Skills → Strategies for Problem-Solving ↓


Guessing and Checking


The "guess and check" strategy is a simple but powerful way to solve math problems, especially when you're just starting out with problem-solving in grade 3 math. This approach allows you to make a reasonable guess at the answer and then check to see if your guess is correct. If the guess isn't correct, you adjust your guess and try again. This strategy helps children learn to think logically and develop their math skills.

Introduction to guessing and checking

Guess and check is exactly what it sounds like. You guess at an answer, calculate whether your guess solves the problem, and then see if your solution is correct. If your guess doesn't solve the problem, you change the guess slightly to see if that helps. Let's start with a simple example.

Example: Finding the secret number

Imagine you are trying to find a number between 1 and 10 that makes an equation true. Suppose the equation is:

x + 3 = 7

You need to find the number for x. Using the guess and check strategy, you pick a number. Let's make 4 guesses and check if it works:

If x = 4, then:

4 + 3 = 7

It works! Our guess is 4 The secret number is 4.

Visual Example

Below is a visual demonstration of estimating and checking with a simple number line:

12345678910

First we made guess 2, which does not solve the equation, then we made guess 4, which does solve the equation. The red circle represents the wrong guess while the green circle represents the correct guess.

Why use guess and check?

Guess and check is especially useful when you don't know how to begin solving a problem. It encourages students to actively engage with the problem and enables them to develop a deeper understanding by trying out different possibilities. It also helps to:

  • Building confidence: Knowing that your first attempt won’t be perfect encourages you to try harder.
  • Improve number sense: Estimating numbers helps you think about how numbers relate to one another.
  • Practicing arithmetic: When checking estimates, you engage in simple mathematical operations.

Steps to estimate and check

The steps are simple, but it pays to be organized:

  1. Understand the problem: Look at the problem carefully. What are you trying to find?
  2. Guess: Choose a reasonable number based on what you know.
  3. Test your guess: Plug your guess into the problem to see if it works.
  4. Revise your estimate: If your estimate wasn't accurate, think about how you could change your estimate to make it better.
  5. Repeat: Keep trying and adjusting until you get the right answer.

Another example: estimating prices

Suppose you have $10 and you want to buy some candy bars costing $2 each. How many candy bars can you buy?

According to the problem, if y represents the number of candy bars, the equation is:

2y = 10

Let's guess and check how many candy bars you can buy.

Respectively

  1. Estimate: Try y = 4. 
    2 * 4 = 8

    It's less than 10, so you can buy more.

  2. New guess: Try y = 5. 
    2 * 5 = 10

    That's exactly 10! You guessed it. You can buy 5 candy bars.

Tips for effective estimating and testing

  • Start simple: Begin with an easy estimate, often in the middle of your range of possibilities.
  • Consider the context: If your guesses are wrong, think about the problem again. Your initial understanding of the problem may need adjustments.
  • Stay organized: Keep track of your estimates and checks to avoid repeating the same mistakes.
  • Use rules of thumb: Sometimes, you know that one number will give you more than you need and another less. Use this information to make better estimates.

Discovering common mistakes

Students may have difficulty with the guess-and-check method if they are not organized or start guessing randomly. Let's look at some common mistakes and learn how to avoid them.

Mistake 1: Guessing at random

One mistake is to pick numbers at random without giving them much thought. For example, if you are given this problem:

5x + 2 = 17

A random number cannot yield a solution, because you are not systematically limiting the options.

How to avoid:

  • Always start with your guess as to what the answer might be.
  • For example, if you know that adding 2 results in 17, the number multiplied by 5 must be close to 3, because 5 * 3 + 2 = 17.

Mistake 2: Not checking properly

Another disadvantage is that an estimate is made but it is not seen whether the estimate works for all parts of the problem. Consider a problem:

2a + 4b = 20

Students may guess that a = 3 and b = 4 but forget to verify by re-entering the equation:

2 * 3 + 4 * 4 = 6 + 16 = 22 (which is > 20)

The estimate should be double-checked with the total numbers in the equation.

Advanced guessing and testing techniques

Eventually, students can become experts in this method and tackle more complex problems, such as arranging, sequencing, or optimizing values. Here are some advanced skills you can discover as you get better at guessing and checking.

Analysis of the problem

Sometimes, breaking problems down into smaller parts can help you estimate more effectively. For example, if you have a problem like this:

x + y = 15
x * y = 56

Let's break it down:

  • Guess the pairs and check which one satisfies both the equations.
  • Example: (7, 8), when 7 + 8 = 15 and 7 * 8 = 56.

Problems related to usage

If the problem at hand seems difficult, relate it to another problem that you already know how to solve. This may give you clues to your estimate.

Closing thoughts

Guessing and checking is a versatile tool in math problem solving. It helps you think analytically and creatively while practicing basic mathematical operations and logical reasoning. Once you start using this method, you'll find how often it can help, not just in math, but in everyday problem-solving situations as well. Keep practicing, and you'll become a pro at guessing and checking in no time!


Grade 3 → 7.1.4


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Making Organized Lists
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Using Logical Reasoning

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Guessing and Checking

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