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 ↓


Using Pictures or Diagrams


In the world of math, especially for young children in grade 3, it can sometimes be challenging to understand concepts and solve problems using numbers alone. An effective strategy to aid this process is to use pictures or diagrams. Visual aids help students understand complex ideas by breaking them down into simpler, more manageable parts. Pictures or diagrams can make abstract concepts concrete, allowing students to visualize problems and identify patterns or solutions that may not be immediately obvious through numbers alone.

Why use pictures or diagrams?

Pictures and diagrams serve as a bridge between the abstract world of numbers and symbols and the concrete world that students experience every day. By translating numerical problems into visual problems, students can interact with them in a more intuitive way. Let's explore some reasons why using pictures or diagrams is beneficial:

  • Visual learning: Many children learn through visual learning. They understand information better by seeing it rather than just hearing or reading it.
  • Engagement: Pictures make learning more engaging and less intimidating. Math becomes a fun challenge rather than a daunting task.
  • Conceptual Understanding: Pictures help students see the connection between numbers and concepts, leading to deeper understanding.
  • Problem classification: Complex problems can be broken down into simpler steps using diagrams, making them easier to solve.

Common types of diagrams

There are many types of diagrams that can be used to help solve math problems. Each type of diagram is best suited for specific types of problems. Below are some common diagrams and how they can be used:

Bar model

A bar model is a diagram that uses bars to represent quantities. Bar models are especially useful for addition, subtraction, multiplication, and division problems. They can help students visualize parts of a whole or compare different quantities.

Imagine a problem where you have 8 apples and you give away 3. How many apples do you have left?

Total apples: 8 Apples given: 3

By drawing a strip showing all 8 apples and shading a portion of it to represent the given 3 apples, students can easily see that the number of remaining apples (5) is the portion of the strip that remains not shaded.

Number lines

Number lines are especially useful for operations such as addition and subtraction, as well as for understanding concepts such as rounding and ordering numbers.

Suppose you want to add 5 and 3 using the number line.

0 5 10 15 20

Starting with 5, you move forward 3 steps to show the addition. This visual method helps students see that the result is 8.

Tally chart

Tally charts are simple diagrams used to record and count frequency. They are useful for organizing data into categories for easy comparison and analysis.

Here is an example of a tally chart to count the types of fruits in a basket.

Apple: ||||
Oranges: |||
Bananas: |||||

Venn diagrams

Venn diagrams are used to show relationships between different sets. These can be useful for showing similarities, differences, and unions of groups.

Set A Set B A ∩ B

In the above diagram, two circles overlap each other. The overlap represents the elements common to both set A and set B (A ∩ B).

Geometry and shape

Geometry is naturally well-suited to visual representation. Shapes such as triangles, squares and circles can be used to explain concepts of more complex ideas such as area, perimeter and symmetry.

rectangle

For example, it may be easier to understand the properties of this rectangle by looking at its lengths and right angles rather than by hearing or reading about it.

Solving word problems using pictures or diagrams

Word problems can be especially challenging for grade 3 students because they require them to translate real-world scenarios into mathematical equations. The use of pictures or diagrams can greatly assist in this translation.

Here's an example of how to use a picture to solve a word problem:

Problem: Sarah has 12 candies. She wants to share them equally with her 3 friends. How many candies will each person get?

  1. Draw a picture that shows 12 candies.
  2. Divide the picture into four equal groups (including Sarah).
Sarah Friend 1 Friend 2 Friend 3

By visualizing this problem and dividing the candies into groups, students can see that each person gets 3 candies.

Conclusion

Pictures and diagrams are invaluable tools in the math classroom, especially for younger students. They provide clarity and a means to understand complex concepts by making the abstract concrete. By incorporating visual strategies into problem-solving, we empower students to approach math problems with confidence and creativity. Whether through bar models, number lines, or other diagrammatic representations, the ultimate goal is for students to develop a strong foundation in mathematical concepts and be able to apply these skills in a variety of scenarios.


Grade 3 → 7.1.1


U
username
0%
completed in Grade 3

← Prev (7.1)
Strategies for Problem-Solving
Next (7.1.2) →
Identifying Patterns in Problems

Comments 



Using Pictures or Diagrams

https://www.buddymath.com/g3/7.1.1?bmal=en