Once students have a grasp of critical thinking, they get that the numbers have real-life connections. Numbers are no longer something school asks them to know, but instead a tool to understand the world around them. With this knowledge, they can start to understand how and why the problems exist, as well as how to find a solution. That’s when number sense comes in. Number sense is a student’s understanding of how numbers work together and are interconnected. It’s how we see that five is a part of ten, or that twelve is made up of ten and two. We build number sense through interaction with concepts such as counting, grouping, and wholes and parts (which leads to fractions).
If Number sense isn’t built up while a student is learning, they’ll find themselves having to do a lot of slow work to find answers, such as counting on their fingers when multiplying or drawing tally marks on their paper for subtraction. Without number sense, solving a word problem that first requires critical thinking and then arithmetic can feel like an impossible task. They’ve done the hard thinking about how the numbers have to connect for the problem, such as getting that they need to multiply instead of divide, but then doing that multiplication becomes an arduous trek of counting, by ones, to a pretty high number.
To students’ dismay, the lack of number sense not only makes the problem harder, but also makes more opportunities for mistakes! So after they’ve spent so much time finding an answer, they may have simply miscounted and still not be right. This leads them to focus mostly on their arithmetic and counting, leaving the critical thinking skills behind, which starts an unhappy cycle of confusion. To avoid that, it’s important to move past habits of finger counting, and practice critical thinking often. Here’s a tougher version of last week’s problem with Suzie to start off that practice. For the young ones, try to do it one piece at a time.
Suzie wants to make apple pies for a picnic. Suzie want to make 6 pies, and the recipe calls for 4 apples for each pie. The store she goes to only sells apples in bags of 8. How many bags of apples does Suzie need to buy?
Answer: Suzie needs to buy 3 bags of apples. Since she wants 6 pies, and each pie needs 4 apples, we need to multiply 6x4, which is 24. The store sells bags of 8, so we need to find how many groups of 8 we need to make 24, which means we divide 24 by 8. This gives us our answer, 3 bags.
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