Last week we talked about 4 number relationships that build number sense in your students. In other words, students with number sense are strong in these number relationships!

Building number relationships is one of those **simple & effective **strategies you can layer on top of the instruction you are already delivering in order to get BIG bang for your buck when it comes to your time with your students.

Because here is the thing. You are welcome to stop teaching [*insert topic here*] and do “number sense work”. But why?

I don’t have the time OR organizational capacity to juggle adding in new activities or units of study that are completely disconnected from the goals I am looking to meet with my students.

And once we open Pandora’s box of “number sense work” are we going to want to stop working towards our goals to do “story problem work” and “fact fluency work” too?

We can and should meld this work together! Let’s take a look at **spatial relationships** and how you can build this number relationship through the instruction you already delivering.

#### Subitizing to Support Fact Fluency (1st Grade Example)

In first grade, you spend a TON of time on developing your students’ understanding of addition and subtraction and beginning to work towards fact fluency. Imagine you are working on facts for 5 (5 + 1, 5 + 2, etc.). In math centers, you introduce a game where students start with a ten frame filled with 5 counters across the top row. Your students spin a spinner and add 1, 2, 3, 4 or 5 to the ten frame. Your students record their work in a number bond and write an equation to match.

Your students will have the support of a ten frame so that they are able to quickly “see” the answer to their equation. This activity supports spatial relationships and allows your students to subitize numbers to 10 in a ten frame. Through this activity, you are BOOSTING your students’ spatial relationships, you are still working towards your goals around understanding addition, you are improving fact fluency and, as an added bonus, you are boosting your students’ awareness of benchmarks of 5 and 10 as well.

It’s a beautiful thing. Isn’t it?

Let’s take a look at another example.

#### Spatial Relationships in Fractions (3rd Grade Example)

In third grade, your students are learning about unit fractions and are composing and decomposing unit fractions and are beginning to compare fractions as well. A roadblock we can anticipate in terms of fraction comparison is that the numbers aren’t intuitive to students relative to the learning they have done in kindergarten through 2nd grade.

For the first time and “8” indicates a SMALLER piece than a “3” when these numbers are in the denominator of a fraction. Building spatial relationships is the answer here.

Consider an activity where students are using fraction strips to build and compare fractions. Your students choose a task card with two different fractions and are asked to build using unit fractions in order to compare. The hands-on material will help your students to develop spatial relationships around fraction numbers. On a recording form, your students color fractions to further steep in the visual representations.

All of a sudden the “roadblock” has been overcome as your students are developing a new schema around fractions and the “confusion” of 8 and 3 having new meaning isn’t so confusing anymore.

Ok. One more.

#### Rounding Decimal Numbers on a Number Line (5th Grade Example)

I’ve written quite a bit about rounding in the past. I am passionate about the idea that most students do not have a *rounding issue *but rather have a *number sense issue. *Students who struggle to round have difficulty identifying benchmark numbers and have further difficulty recognizing which of those benchmark numbers is closer to the number they are rounding.

Build spatial relationships around decimal numbers by building a life-sized number line! Hang a string across two cabinets or along the whiteboard. Prepare number flags with numbers spanning between two decimal numbers (ex: 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 1.0). Hand these number flags to your students out of order and ask your students, one at a time, to use a clothespin to hang the flag on the number line in the place where they think that number would go.

In early attempts at this activity, you will find that your students will need to move and slide numbers as they go. In later attempts, you will find that your students’

**spatial relationships **have developed and your students have better sense of which numbers are closer or farther apart on a number line.

Your students’ internal number lines are strengthened when they work with number lines that they can see and touch in real life because your students strengthen their spatial relationships through interaction.

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