## 4th Grade Math Operations and Algebraic Thinking

With every grade level students are required to complete more challenging computational problems.

In fourth grade students must be able to:

- Solve multi-step problems involving addition, subtraction, multiplication, and addition.
- Understand number factors for numbers less than 100.
- The factors of 50 include 25, 2, and 5x 10, and since 10 is 5 x 2, this means that 5x5x2 is 50. 25 is a factor of 50 but it is not prime so it can be reduced farther to 5 x 5. So the prime factors of 50 are 5, 5, and 2.

- Generate and identify patterns in numbers.

CCSS.MATH.CONTENT.4.OA.A.1| Use the four operations with whole numbers to solve problems.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Standards: 4.OA.A.1:

**Understanding Multiplicative Comparisons (4.OA.A.1)**In fourth grade, students learn to interpret multiplication equations as comparisons. For example, the equation

35=5×735 = 5 \times 735=5×7 indicates that 35 is 5 times as many as 7. Visual aids, such as comparison bars or arrays, can be extremely helpful in conveying this concept. Here’s a sample exercise: Draw an array to show 4×64 \times 64×6 and interpret it as 4 groups of 6 or 6 groups of 4.

CCSS.MATH.CONTENT.4.OA.A.2| Use the four operations with whole numbers to solve problems.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Standards: 4.OA.A.2:

**Solving Multiplicative Comparison Word Problems (4.OA.A.2)**

When it comes to solving word problems involving multiplicative comparisons, a step-by-step approach can be effective. Here’s an example: “Lisa has 3 times as many apples as Tom. If Tom has 5 apples, how many apples does Lisa have?”

- Step 1: Identify the quantities and the relationship (Tom’s apples = 5, Lisa’s apples = 3 times Tom’s).
- Step 2: Write the equation $3×5=15$.
- Step 3: Solve the equation to find Lisa’s apples.

CCSS.MATH.CONTENT.4.OA.A.3| Use the four operations with whole numbers to solve problems.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Standards: 4.OA.A.3:

**Multistep Word Problems (4.OA.A.3)**

Multistep problems can be broken down using real-life scenarios. For example: “Sarah bought 3 packs of markers. Each pack contains 4 markers. She also bought 2 notebooks. How many items did Sarah buy in total?”

- Step 1: Calculate the total markers $3×4=12$.
- Step 2: Add the notebooks $12+2=14$.
- Step 3: Therefore, Sarah bought 14 items in total.

Emphasize checking the reasonableness of answers using estimation strategies like rounding. For instance, if the numbers involved were large, round them to the nearest ten to see if the solution is reasonable.

CCSS.MATH.CONTENT.4.OA.B.4| Gain familiarity with factors and multiples.

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Standards: 4.OA.B.4:

**Factors and Multiples (4.OA.B.4)**

Finding all factor pairs of numbers from 1 to 100 and recognizing prime and composite numbers are key skills. For example:

- Factor pairs of 24: $1×24,2×12,3×8,4×6$.
- Explain that a prime number has only two factors, 1 and itself (e.g., 7), while a composite number has more than two factors (e.g., 12).

Create engaging activities like factor pair puzzles or games. For instance, use a number grid to circle prime numbers and mark composite numbers.

CCSS.MATH.CONTENT.4.OA.C.5| Generate and analyze patterns.

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Standards: 4.OA.C.5

**Generating and Analyzing Patterns (4.OA.C.5)**

Students learn to generate and analyze patterns by following a simple rule. For example, starting with 2 and adding 3 repeatedly: $2,5,8,11,14,…$. Encourage them to identify patterns and predict the next numbers or shapes. Use visual patterns and interactive tools to make learning engaging.

**Practical Application**

Applying math concepts to real-life situations helps reinforce learning. For example:

- Use factors and multiples to solve problems like dividing a group of items evenly.
- Recognize patterns in nature or art, which is also foundational in coding and design