Addition and subtraction strategies (age 7+)

This workbook helps grown-ups understand arithmetic deeply so they can teach it well. It is all about place value, which means knowing that in a number like 47, the 4 stands for 4 tens and the 7 stands for 7 ones. It also teaches thinking strategies, which are clever ways to add and subtract in your head. One big idea is that you can explain the steps of a written method. When you add 36 plus 25, you can say: 3 tens plus 2 tens is 5 tens, and 6 ones plus 5 ones is 11 ones, which is 1 ten and 1 one, so we get 61. Every step has a reason, and place value is the reason. The same ideas help with subtracting, rounding, and working with fractions and decimals later on.

Sometimes you need to do math in your head, with no calculator and no paper. Break the problem into parts. Treat the hundreds, the tens, and the ones like little separate problems. If you want to add 48 and 35, first add the tens: 40 plus 30 is 70. Then add the ones: 8 plus 5 is 13. Then put the parts together: 70 plus 13 is 83. You can do the same thing when you subtract. Breaking numbers into tens and ones works because each part keeps its own value, so nothing gets lost along the way.

This is a list of video lessons for grade 4 math. The first big module is called Place Value, Rounding, and Algorithms for Addition and Subtraction. An algorithm is just a careful step-by-step method, like the column method you write on paper. The videos show why each step of the method works. They explain that when you line up the columns, the ones are above the ones and the tens are above the tens, so each digit only ever meets digits from its own place. That is why adding the columns one at a time gives the correct answer. The module also connects this to rounding numbers to the nearest ten or hundred.

Some word problems take two steps to solve. First you might add to find a total, then subtract to find what is left. Knowing place value makes each step feel easy. If a problem says a shop had 56 pencils and sold 23, you can think in tens and ones. 5 tens take away 2 tens leaves 3 tens, and 6 ones take away 3 ones leaves 3 ones, so 33 pencils are left. You can even estimate first by rounding 56 to 60 and 23 to 20, so you expect an answer near 40, and 33 is close. Checking your answer with place value helps you catch mistakes.