Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Understanding Addition Keywords: In word problems, look for terms like 'total', 'sum', 'altogether', 'plus', 'in all', or 'combined'. These words signal that you should combine two or more quantities. Imagine a 'Part-Part-Whole' bar model where two smaller blocks are placed side-by-side to form one long bar representing the total.
Understanding Subtraction Keywords: Look for terms like 'difference', 'left', 'remaining', 'how many more', 'how many fewer', or 'exceeds'. These words indicate you are finding the gap between numbers or removing a part from a whole. Visualize a long bar with a section shaded or cut out to show what remains.
Place Value Alignment: When solving word problems vertically, always align digits according to their place value: Ones under Ones, Tens under Tens, Hundreds under Hundreds, and so on. Imagine vertical grid lines separating each column to ensure digits don't shift.
Regrouping in Addition (Carrying): If the sum of digits in a column is or more, you must 'carry over' the tens digit to the next column on the left. For example, if the Ones column sum is , write in the Ones place and carry to the Tens place.
Regrouping in Subtraction (Borrowing): If the top digit (minuend) is smaller than the bottom digit (subtrahend), you must borrow from the next higher place value. Visualize taking one 'Ten' block and breaking it into ten 'Ones' blocks to make the subtraction possible.
Multi-Step Word Problems: Some problems require more than one operation. For instance, you might need to add two amounts first and then subtract the total from a larger number. Always read the problem twice to identify the sequence of events.
Estimating to Verify: Before calculating the exact answer, round the numbers to the nearest or to get an approximate result. This helps you check if your final answer is reasonable. On a number line, see which 'ten' or 'hundred' the number is closest to.
The Inverse Relationship: Addition and subtraction are opposites. You can check a subtraction problem by adding the answer (difference) back to the number you took away (subtrahend). If the sum equals the original starting number (minuend), your calculation is correct.
📐Formulae
💡Examples
Problem 1:
A poultry farm produced eggs on Monday and eggs on Tuesday. How many eggs were produced in total over the two days?
Solution:
Step 1: Identify keywords. 'In total' indicates addition. Step 2: Set up the calculation: . Step 3: Add the Ones: . Write , carry . Step 4: Add the Tens: . Step 5: Add the Hundreds: . Write , carry . Step 6: Add the Thousands: . Total = .
Explanation:
We combined the production numbers for both days using addition with regrouping in the Ones and Hundreds places.
Problem 2:
A water tank has a capacity of liters. If liters of water are used, how much water is left in the tank?
Solution:
Step 1: Identify keywords. 'How much is left' indicates subtraction. Step 2: Set up the calculation: . Step 3: Subtract Ones: Cannot subtract from , borrow from Thousands. becomes . Step 4: (Ones). Step 5: (Tens). Step 6: (Hundreds). Step 7: (Thousands). Remaining water = liters.
Explanation:
Since the minuend had zeros in the ones, tens, and hundreds places, we performed 'subtraction across zeros' by regrouping from the thousands place.