"Math Today! That's not how i learned!"
aka... homework help: how you can help your child show work
There are several ways we ask your child to show their math thinking. As per the common core we are building the foundation for algebraic knowledge. But shhh! don't tell your 3rd grader that. We wouldn't want to stress them out needlessly. However, what this means is students are being asked to explain how they arrived at an answer and why it works. Therefore, they need a stronger sense of how numbers work within our base 10 system.
Since skill and drill isn't the focus just yet, the trusty old algorithm isn't taught until 4th grade. In class, we ask students not to use the algorithm to solve because it doesn't explain why or how they arrived at the answer. For students who are ready for the challenge, we still insist that they use a second way from below to prove their answer. Below are the ways we teach students to show their math thinking. Please note that not every child will need or find every way useful. However, in order to reach all learners we provide the following as options:
Base 10 blocks
This is a visual representation of our base 10 system. It concretely links students to the place value associated with the addition or subtraction of numbers. Students can build or draw up to the landmark numbers of tens, hundreds, and thousands to build a foundation of why regrouping or borrowing happens between columns in later years.
Number line
This is a faster visual model for students to make jumps at first in chunks of numbers they understand. Ex. 2, 5,10. By third grade your child should begin to take jumps of 10, 20, or even 60. This is the first step to being able to break apart numbers mentally because students are visual making jumps to the nearest landmark number (tens, or hundreds) and then they are able to make larger jumps from there. This works well for both addition and subtraction.
Expanded form addition
Case studies have shown that kids developmentally read math equations or algorithms in the same direction as they are learning to read. This is why kids often want to start with the hundreds and work towards the ones. We adults know this will always end up in heartbreak. The expanded from addition method meets kids in the middle. Students are asked to place both numbers being added into expanded form. Then they add each place value together. In the end they add together all sums found for their answer. This can be tricky for subtraction as students might forget that even when subtracting you must add your place value answers together.
Please check out this video if you want further explanation. Youtube.
Break Apart
Break apart numbers and add them to the other addend to reach landmark numbers. This is very useful for quick mental math. Disclaimer: We all don't get here and some of us will still need pencil and paper. A great way to practice this and see it in action is on Greg Tang's website play the game Break Apart. Subtraction Example YouTube
Since skill and drill isn't the focus just yet, the trusty old algorithm isn't taught until 4th grade. In class, we ask students not to use the algorithm to solve because it doesn't explain why or how they arrived at the answer. For students who are ready for the challenge, we still insist that they use a second way from below to prove their answer. Below are the ways we teach students to show their math thinking. Please note that not every child will need or find every way useful. However, in order to reach all learners we provide the following as options:
Base 10 blocks
This is a visual representation of our base 10 system. It concretely links students to the place value associated with the addition or subtraction of numbers. Students can build or draw up to the landmark numbers of tens, hundreds, and thousands to build a foundation of why regrouping or borrowing happens between columns in later years.
Number line
This is a faster visual model for students to make jumps at first in chunks of numbers they understand. Ex. 2, 5,10. By third grade your child should begin to take jumps of 10, 20, or even 60. This is the first step to being able to break apart numbers mentally because students are visual making jumps to the nearest landmark number (tens, or hundreds) and then they are able to make larger jumps from there. This works well for both addition and subtraction.
Expanded form addition
Case studies have shown that kids developmentally read math equations or algorithms in the same direction as they are learning to read. This is why kids often want to start with the hundreds and work towards the ones. We adults know this will always end up in heartbreak. The expanded from addition method meets kids in the middle. Students are asked to place both numbers being added into expanded form. Then they add each place value together. In the end they add together all sums found for their answer. This can be tricky for subtraction as students might forget that even when subtracting you must add your place value answers together.
Please check out this video if you want further explanation. Youtube.
Break Apart
Break apart numbers and add them to the other addend to reach landmark numbers. This is very useful for quick mental math. Disclaimer: We all don't get here and some of us will still need pencil and paper. A great way to practice this and see it in action is on Greg Tang's website play the game Break Apart. Subtraction Example YouTube