Jacob used place value blocks to show how to add 243 and 688. What is the sum?
For the first number, 243, we have 200 blocks, four tens blocks, and three ones blocks. When we look at the number 688, we have six hundreds, eight tens, and eight ones. Jacob has taken these blocks and regrouped them to help represent the sum.
Jacob counted out 10 ones and he grouped them together: one, two, three, four, five, six, seven, eight, nine, 10. He stacked them up and made one tens block. Those blocks have been removed from the ones and placed in the tens. There is now one ones block and one tens block.
In our addition problem, we represent that like this: one ones and one 10. Now we look at the tens block and we see that Jacob has done even more grouping. He has counted 10 tens and turned them into 100: one, two, three, four, five, six, seven, eight, nine, and 10. When you take these 10 tens blocks and put them together, you have 100 block.
We’ve moved the 10 tens block out of the tens place and into the hundreds place. That leaves us with three tens and one new hundreds. We represent that in our addition problem by saying we have three tens and carrying over the one into the hundreds place, three tens and 100.
Our final step is in the hundreds place. We need to add up how many hundreds we have: one, two, three, four, five, six, seven, eight, nine. That means that our 200 plus our 600 plus the carried over 100 gives us a total of 900. Using place value blocks, we’ve demonstrated that the sum of 243 and 688 equals 931.