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 ↓


Making Organized Lists


Let's talk about a way to solve problems in math that we call "making organized lists." This is a strategy that can help us find solutions when our minds have a lot of possibilities to think about. When we organize our thoughts and ideas into a list, it becomes much easier to see what we need to do and find a solution without missing out on anything important.

What is organized list?

An organized list is a way of arranging information systematically. In simple terms, it means writing things down in a clear and well-organized order. An organized list helps us not to forget any step or possibility when solving a math problem, especially problems that have different possible answers. When you create an organized list, you take a large set of data or possibilities and make them manageable, clear, and easy to understand.

Why create organized lists?

Making organized lists is helpful in many ways. Here are some reasons why this is a useful strategy:

  • Don't miss steps: When solving a problem with multiple steps or options, it's easy to miss something. Making a list helps ensure that you consider every possibility.
  • Clear thinking: Writing things down on paper helps organize thoughts, making a problem seem less overwhelming.
  • Easy to review: Lists make it easy to check for mistakes by reviewing your work again.
  • Easier problem solving: When you see everything up front, finding the right answer is often simple and quick.

How to create an organized list

To create an organized list, you need to gather all the information and questions related to your problem. Here are some steps to guide you:

  1. Understand the problem: Read the problem carefully and understand clearly what is being asked.
  2. Identify the possibilities: Determine all of your possibilities or options.
  3. Organize your list: Arrange your possibilities in a particular order. This could be numerical order, alphabetical order, or some other logical order, depending on your problem.
  4. Evaluate each option: Look at each item on your list, and evaluate how it fits into solving the problem.
  5. Determine the solution: Decide which possibility gives you the right answer or helps you understand the problem better.

Examples of creating organized lists

Example 1: Finding all combinations

You have 2 shirts and 3 different pants. How many different clothes can you make?

To solve this problem, let's create an ordered list. Here, shirts can be labeled as S1 and S2, and pants can be labeled as P1, P2, and P3. We will list all the possible combinations of shirts and pants:

1. S1, P1 2. S1, P2 3. S1, P3 4. S2, P1 5. S2, P2 6. S2, P3

So, there are 6 possible outfits created when you wear the shirt and pants together.

Example 2: Arranging numbers

Suppose you have the numbers 1, 2 and 3, and you want to know in how many different ways you can arrange these numbers.

Let's make a systematic list to find all the permutations:

1. 1, 2, 3 2. 1, 3, 2 3. 2, 1, 3 4. 2, 3, 1 5. 3, 1, 2 6. 3, 2, 1

We found 6 different ways to arrange the numbers 1, 2 and 3.

Example 3: Using systematic lists to solve word problems

Here's a fun word problem: Sarah has 4 different kinds of muffins to choose from, and she wants to pack 2 different muffins in the lunchbox. How many ways can she do this?

We can solve this problem by listing all possible pairs of muffins:

1. Muffin A, Muffin B 2. Muffin A, Muffin C 3. Muffin A, Muffin D 4. Muffin B, Muffin C 5. Muffin B, Muffin D 6. Muffin C, Muffin D

By listing we can see that there are 6 different ways to choose 2 out of 4 muffins.

Visual example: understanding lists with shapes

Let's look at a visual example. Suppose you have 3 different colored circles (red, blue, green) and you need to create all possible pairs of circles.

Pair 1: Red, BluePair 2: Red, GreenPair 3: Blue, Green

Challenges in creating organized lists

Making organized lists is a helpful strategy, but it can be a little tricky at times. Here are some challenges and how to deal with them:

  • Too many possibilities: When there are too many possibilities, lists can become long and confusing. It's important to stay organized, perhaps organizing the lists into subcategories.
  • Missing options: Sometimes, it's easy to miss options. Double-check your work to make sure all possibilities are listed.
  • Staying organized: It's important to keep your list neat and tidy. Use numbers, bullet points, or tables to keep your items organized.

Practice activity: try making your own organized list

Now, you try! Imagine you are planning a meal, and you can choose 1 main dish from chicken, beef or fish, and 1 side dish from rice, salad or potatoes. How many meal combinations can you make? Write down an organized list to find out!

Here's a hint to get you started: Start by choosing chicken, and make a list of all the possible side dishes you could eat with it. Then, move on to beef and fish.

Conclusion

Making organized lists is more than just keeping items in order. It's a powerful tool in math problem-solving that helps us handle complex information and make sure we're considering all of our options. When you practice this skill, you'll become better at thinking logically and critically which can help in both math and everyday situations. So the next time you're faced with a problem with many different possible answers, try making an organized list to find the solution!


Grade 3 → 7.1.3


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Making Organized Lists

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