STAAR Grade 4 Math

Addition combines quantities. The numbers being added are called addends. The result is called the sum.

For multi-digit addition, align numbers by place value. Add column by column from right to left. When a column sum is 10 or greater, regroup (carry) to the next column.

Add 4,587 + 2,946. Start with ones: 7 + 6 = 13. Write 3, carry 1. Tens: 8 + 4 + 1 = 13. Write 3, carry 1. Hundreds: 5 + 9 + 1 = 15. Write 5, carry 1. Thousands: 4 + 2 + 1 = 7. The sum is 7,533.

Addition properties include the commutative property (changing the order of addends does not change the sum: 5 + 3 = 3 + 5) and the associative property (changing the grouping of addends does not change the sum: (2 + 3) + 4 = 2 + (3 + 4)). The identity property states that adding zero to any number gives that number: 7 + 0 = 7.

Subtraction finds the difference between quantities. The starting amount is the minuend. The amount being taken away is the subtrahend. The result is the difference.

For multi-digit subtraction, align numbers by place value. Subtract column by column from right to left. When the top digit is smaller than the bottom digit, regroup (borrow) from the next column.

Subtract 5,032: 1,758. Start with ones: 2 - 8. Cannot subtract. Borrow from tens. But tens digit is 3. Borrow from hundreds. But hundreds digit is 0. Borrow from thousands. The 5 becomes 4. The 0 becomes 10. Borrow from that 10 for hundreds: 10 becomes 9, and hundreds digit becomes 10. Borrow from that for tens: it becomes 9, and tens digit becomes 12. Now subtract: Ones: 12 - 8 = 4. Tens: 9 - 5 = 4 (after adjustment). Hundreds: 9 - 7 = 2. Thousands: 4 - 1 = 3. The difference is 3,274.

Subtraction can be checked using addition: difference + subtrahend = minuend. For the problem above, 3,274 + 1,758 = 5,032.

Multiplication is repeated addition. The numbers being multiplied are called factors. The result is called the product.

For multiplying by one-digit numbers, multiply the single digit by each digit of the larger number, working from right to left. Regroup as needed.

Multiply 347 × 6. Ones: 7 × 6 = 42. Write 2, carry 4. Tens: 4 × 6 = 24, plus 4 = 28. Write 8, carry 2. Hundreds: 3 × 6 = 18, plus 2 = 20. Write 20. The product is 2,082.

For multiplying by two-digit numbers, use partial products. Multiply by the ones digit first, then multiply by the tens digit (shifting one place left), then add the partial products.

Multiply 47 × 23. First partial product: 47 × 3 = 141. Second partial product: 47 × 20 = 940. Add: 141 + 940 = 1,081.

Multiplication properties include the commutative property (4 × 7 = 7 × 4), associative property ((2 × 3) × 5 = 2 × (3 × 5)), identity property (any number times 1 equals that number), and zero property (any number times 0 equals 0). The distributive property connects multiplication and addition: 6 × 23 = 6 × (20 + 3) = (6 × 20) + (6 × 3) = 120 + 18 = 138.

Division separates a quantity into equal groups. The total being divided is the dividend. The number of groups (or size of groups) is the divisor. The result is the quotient. Any amount left over is the remainder.

Division facts are related to multiplication facts. Since 7 × 8 = 56, we know 56 ÷ 7 = 8 and 56 ÷ 8 = 7.

For dividing by one-digit numbers, use long division. Divide, multiply, subtract, bring down, and repeat.

Divide 846 ÷ 3. How many times does 3 go into 8? Two times (2 × 3 = 6). Write 2 above the 8. Subtract: 8 - 6 = 2. Bring down 4 to make 24. How many times does 3 go into 24? Eight times. Write 8 above the 4. Subtract: 24 - 24 = 0. Bring down 6. How many times does 3 go into 6? Two times. Write 2 above the 6. Subtract: 6 - 6 = 0. The quotient is 282.

When division does not come out evenly, the remainder is written as "R" followed by the remainder value. For 847 ÷ 3, the quotient is 282 R1.

Division can be checked using multiplication: (quotient × divisor) + remainder = dividend. For 847 ÷ 3 = 282 R1: (282 × 3) + 1 = 846 + 1 = 847.

In word problems, remainders must be interpreted based on context. There are three common scenarios.

Drop the remainder when the question asks how many complete groups. If 25 students go on a trip and each van holds 6 students, how many full vans are there? 25 ÷ 6 = 4 R1. There are 4 full vans.

The remainder is the answer when the question asks what is left over. If you have 25 stickers and put 6 on each page, how many stickers are on the last page? The answer is 1.

Estimation helps check if answers are reasonable. Round numbers to friendly values, then compute mentally.

Estimate 4,892 + 3,156. Round to nearest thousand: 5,000 + 3,000 = 8,000. The actual sum (8,048) should be close to this estimate.

Estimate 78 × 42. Round to nearest ten: 80 × 40 = 3,200. The actual product (3,276) should be close to this estimate.

For front-end estimation with addition, use only the leftmost digits. For 4,892 + 3,156, use 4,000 + 3,000 = 7,000.

Compatible numbers are numbers that are easy to compute mentally. For 248 ÷ 5, think 250 ÷ 5 = 50.

When a problem contains multiple operations, follow a specific order. Fourth graders need to understand that multiplication and division are performed before addition and subtraction, working left to right. Parentheses are always done first.

Word problems require identifying the correct operation. Key words can help, but context is most important.

Addition situations include combining groups, finding totals, and increasing quantities. Subtraction situations include taking away, finding differences, and comparing quantities. Multiplication situations include equal groups, arrays, area, and scaling. Division situations include sharing equally, making equal groups, and finding how many groups.

Multi-step problems require two or more operations. Read carefully, identify what is being asked, determine the steps needed, and solve systematically.

A store has 8 boxes of pencils with 24 pencils in each box. They sell 45 pencils. How many pencils remain? Step 1: Find total pencils. 8 × 24 = 192. Step 2: Subtract pencils sold. 192 - 45 = 147 pencils remain.

The STAAR exam tests computation through both straightforward calculation problems and word problems. Students must demonstrate fluency with basic facts and proficiency with algorithms. Multi-step problems are common. Questions may ask students to identify which operation to use, estimate before calculating, or interpret remainders appropriately.