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 ↓


Breaking Down Problems into Steps


Problem-solving in math is an essential skill that can be developed by learning to break down problems into manageable steps. This technique is especially useful for younger learners, such as those in grade 3, who are just beginning to tackle more complex math problems. The ability to break down a problem into smaller, more digestible parts allows students to tackle each section with focus and confidence, paving the way to finding a solution.

Breaking down problems is like solving a puzzle. Every step is like a piece of the puzzle, and when all the pieces are put together in the right way, the whole picture or in this case the solution emerges. To explain how this is done, let’s look at some structured approaches and examples.

Step-by-step strategy

Let's explore a simple math problem using a step-by-step strategy:

Example: Counting the total number of apples

Suppose Jim has 5 apples and his friend gives him 3 more apples. How many apples does Jim have now?

  1. Understand the problem: Before attempting to solve the problem, it is important to understand what is being asked. Here, we need to find the total number of apples Jim has.
  2. Plan the solution: In this case, we can add the number of apples Jim originally had (5) to the number of apples he received (3).
  3. Execute the plan: Calculate and sum up: 
    5 + 3 = 8
    So, Jim now has 8 apples.
  4. Check the solution: Finally, verify the answer to make sure it makes sense. Counting the apples again confirms that 5 apples and 3 apples add up to 8 apples.

Visual representation

It is also beneficial to use visual aids to simplify the problem-solving process. Below is a visual example depicting the apple problem:

,

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Example: Handing out candies

Tim has 12 candies and wants to divide them equally among three friends, including himself. How many candies will each person get?

  1. Understand the problem: We want to determine how many candies each person will get when 12 candies are divided equally among four people.
  2. Plan the solution: Since this is a case of division, we divide the total candies by the number of persons. 
    12 ÷ 4
  3. Execute the plan: Solve the division by: 
    12 ÷ 4 = 3
    Each person will get 3 candies.
  4. Check the solution: Multiplying the result by the number of people gives the total number of candies: 
    3 x 4 = 12
    The solution is correct.

The benefits of breaking down problems

Breaking down a complex problem into smaller parts not only makes it easier to find a solution, but also provides many educational benefits:

  • Increased understanding: Analyzing a problem allows students to better understand each element of the task.
  • Less anxiety: Smaller, less cumbersome steps help build confidence and reduce anxiety when solving math problems.
  • Better Focus: Students can focus on solving one part of the problem at a time.
  • Skill development: Each step in the process can help develop specific mathematical skills (e.g., addition, subtraction, division).

More examples

Example: Calculating total cost

Sarah bought a book for $7 and a pen for $2. How much did she spend in total?

  1. Understand the problem: Find the total cost of the items purchased by adding up their prices.
  2. Plan the solution: Add up the cost of the book and the pen. 
    7 + 2
  3. Implementation of the plan: Calculate the amount: 
    7 + 2 = 9
    In total, Sarah spends $9.
  4. Check the solution: Make sure the calculations are in accordance with the verification method.

These basic exercises establish a strong foundational understanding of mathematical relationships and foster a strategic approach to tackling more important and complex problems in the future.

Conclusion

Mastering the skill of breaking down problems into smaller, manageable steps increases mathematical fluency and promotes a deeper understanding of various math concepts. This skill is not limited to just math; it has practical applications in many subjects and everyday tasks. Developing problem-solving skills at an early age empowers students, giving them the ability and confidence they need to effectively tackle academic and real-life challenges.

Applying a systematic approach to problem-solving fosters critical thinking and develops a balanced method for assessing, analysing and solving mathematical problems – an invaluable skill for young learners that they will carry with them throughout their education and into adulthood.


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Breaking Down Problems into Steps

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