Question

1. solve 667 + 295 using two different strategies.

a.
b.
c. explain which strategy you prefer to use when solving and why.

Explanation:

Part a: Strategy 1 - Standard Addition

Step1: Align digits by place

Align 667 and 295 by their ones, tens, and hundreds places:

  667
+ 295
------

Step2: Add ones place

Add the ones digits: \(7 + 5 = 12\). Write down 2 and carry over 1 to the tens place.

Step3: Add tens place

Add the tens digits and the carried over 1: \(6 + 9 + 1 = 16\). Write down 6 and carry over 1 to the hundreds place.

Step4: Add hundreds place

Add the hundreds digits and the carried over 1: \(6 + 2 + 1 = 9\).

Step5: Combine results

Combining the digits, we get \(667 + 295 = 962\).

Part b: Strategy 2 - Compensation (Rounding)

Step1: Round 295 to 300

Since 295 is close to 300, we can first add 300 to 667: \(667 + 300 = 967\).

Step2: Adjust for over - addition

We added 5 more than we should have (because \(300 - 295 = 5\)), so we subtract 5 from the result: \(967 - 5 = 962\).

Part c: Preference Explanation

I prefer the compensation strategy (used in part b) because it simplifies the addition by using a round number (300) which is easier to add mentally. After adding the round number, the adjustment (subtracting 5) is a simple operation. This strategy reduces the chance of making errors with carrying over digits as in the standard addition method, especially when dealing with numbers close to multiples of 10 or 100.

Answer:

a. Using standard addition, \(667 + 295 = 962\)
b. Using compensation, \(667 + 295 = 962\)
c. Preference: Compensation strategy (e.g., for simplicity in mental calculation).