Developing Strong Number Sense with Eureka Math

One of the most important aspects of Eureka Math is how heavily the skills rely on the foundation of number sense.

​Each grade level begins the school year with a module that will provide the strategies students will need to help the future lessons build upon the concepts.

Keep this in mind when working with your team to modify the timeline or shift modules. If needed, try to work on getting the beginning foundational skills in as priority. It will help you with teaching the other modules when they arrive.
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Some number sense concepts will be taught early on and then taught again later using larger numbers. Here are some of the building blocks needed early in the program to provide a strong number sense foundation.

As a teacher, it is important to become familiar with these concepts yourself and “reteach” your mind to also become fluent in these strategies. Before I teach a lesson, I practice it out first to make sure I am following this method and not letting any of my own previous math knowledge sway the way I model the concepts.

Fluency Addition and Subtraction Concepts

Number Bonds

A number bond is three circles connected by two lines in a triangle formation. The number at the top is the whole and the other two numbers are the parts. This model shows students how numbers are connected and related. When using the number bonds, students will use language to help them make understanding of the facts that are related. For example in a number bond of 6+4=10, students can say, “I know 6+4=10.” They can also say, “I also know 10-6=4.” Students can look at the number bond in a variety of ways. They eventually become fluent enough with the facts that they can visually know a missing number in a number bond.

Adding Like Units

When students are learning adding strategies, they are taught to use ten as a benchmark. Working with the number bond strategy, students can extend numbers to a tens place. For example to solve 20+7=____ , students can think 2 tens plus 7 ones equals 2 tens and 7 ones to equal 27. This strategy is adding like units. When students begin adding larger numbers such as 20+34=____, they can add the ones and think 0+4=4 and then add the tens 20+30= 50. Then add 50+4=54. Adding like units across is taught before adding vertically in an algorithm. This helps students to understand the concept of place value along with adding and not just memorizing steps to add.

Making Ten

When adding fluently, students use ten as a benchmark to make it easier to add on. For example, to solve 8+7=15, students can make a number bond for 7 and show 5 and 2. Now, they can think, 8 is closer to 10 than 7, so I can make 10 with 8. The next step is to add 8+2=10. Now, that 5 is still left from the number bond, so the last step is to add 10+5=15. This is a visual strategy at first, but after practicing it becomes a mental math strategy.

​Take out Ten

This strategy helps students see the tens as a benchmark and to subtract fluently. For example, students start out practicing how to create a number bond with a number larger than ten. For example, 17 would be a number bond using 7 and 10. This is helpful to know before beginning to add and subtract using the take out ten strategy. In this strategy students are taught to look at 14-9=_____ and make a number bond for 14, using 4 and 10. They have now pulled out the ten and are showing the ones left. Now, students solve 10-9=1, then add 1+4=5. The final answer is 5. This is pulling together so many number sense skills. Students can ring together the numbers they are going to subtract first, then add the numbers that are left. Showing all of the work with the number bond and equations will be a way for students to show their thought process to problem solve.

These foundational fluency concepts may seem like strange way to go about traditional adding and subtraction, but there is something special about this way of thinking. I have found that students take ownership of these skills very early on. It becomes a way for them to truly know what numbers are made up of and what exactly the process of addition and subtraction are. They have a deeper understanding very early on and it will help build our strong math students with deep number sense. This is much more valuable than just memorizing a system of adding and subtraction. This is what makes Eureka Math such a valuable asset to any math curriculum!