Do you have students who are struggling in math because of under-developed number sense? Do your students lack a solid understanding of how numbers work? In this post, I will share 3 things you can do to help these students increase and improve their number sense.
Teach with Problem Solving
It is critical that as teachers, we shift from the traditional practice of modeling “how to do math.” Mathematics instruction is much more effective when we use a problem-based approach (Van De Walle & Loven). Allowing students to struggle with any task is hard for teachers (so hard!) But it is so important that we allow this to occur in math. Instead of teaching a strategy and saying “now use this strategy to solve this problem,” try posing the problem first at the beginning of your lesson. This will allow students to engage in analytical thinking and reflective thought, which is crucial to a solid understanding.
For example: Let’s look at a lesson on decomposing the number five. I could begin the lesson giving students red and yellow counters and showing them how to put the counters in a cup, shake it up, and count the yellow and the red to “see” that the two sets shows a way to make five. Then the students could practice it, sharing out the ways they made five.
What was wrong with the lesson above? It was a great hands-on way to have students explore numbers. But what is the activity really focusing on? I would argue that the focus on the lesson above is the procedure of shaking the cup, dumping the counters, counting the colors. What if instead of starting with the activity, this problem was posed instead?
“Boys and girls, I just ordered my mom a flower arrangement for Mother’s Day. I know that it has five flowers, and some flowers are red and some are yellow. I’m trying to figure out what the flower arrangement might look like. How many could be red? How many could be yellow?” Allow the class to figure out ways you could solve this problem. Some students might draw. Some students might use fingers or manipulatives. Some students will get it wrong and that’s OK. Students share out their ideas and you record them on chart paper. This problem-based approach will help students “get” what you are doing when you decompose the number five using those counters.
Next time you plan a math lesson, think about how to can flip it to begin with a problem. My problem solving every day pack includes many different types of problems which support number sense.
Number Sense Routines
If you teach primary, then you probably already have some routines in place that support number sense. Your calendar routine, counting on the hundreds chart, and graphing the daily weather are all such routines. Adding in additional activities that support seeing and conceptualizing quantities can provide a huge boost in the number sense of your whole class. If your calendar time is separate from your math block, having a daily math warm-up prior to your main lesson is where you will do these activities.
Here are some number sense routines to try:
- Quick Images with dot cards
- Ten frame flash
- Rekenrek games
- Count around the circle
The book Number Sense Routines, by Jessica Shumway, is filled with these strategies and more which support number sense to add to your math block (affiliate link below).
A number talk is a short discussion between you and your students about a math problem that you have shown. Your students will solve the problem mentally and will then share out their thinking about the process. In kindergarten, I always start with dot cards. “What number did you see? How did you see it? What did you notice?” Open it up to allow other students to share out. Some students may have seen six right away because they saw 2 groups of 3 and know that 3 and 3 make six. Another student may have seen the first group of three and then counted on. Another student may have counted by ones. Hearing other students’ strategies (and misconceptions, which is often even more powerful) is an important component of an effective number talk. For more information about number talks, check out the book Number Talks (affiliate link).
Throughout all of these activities, the conversation is key. Having students explain their thinking, working through misconceptions together, and reflecting on what was learned will have a profound effect on your students’ number sense.