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Math and Success Adds Up

Rocklin Unified School District

Math andSuccess Adds UpRocklin Unified School District

GRADES TK-5: 2nd Edition 2022-2023

Math and Success Adds Up, Grades TK-5, is a newsletter for parents of children in transitional kindergarten through fifth grade. Each publication will include information on how parents can support and foster the love of math at home.

The Best Way to Support a Strong Foundation in Math

I love this quote above from Howden. Number Sense is so important at the elementary level. Math is not about rules and memorization. It is about making and building connections with numbers. One of the best things you can do to support math learning at home is to provide students opportunities to build their number sense. Spend time exploring with manipulatives, playing games, and discussing problem solving strategies with your child. You can support your child's number sense development in just a few short minutes each day.
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Use Manipulatives

Using counters of any kind is helpful. Use coins, blocks, legos, buttons, keys, rocks, ANYTHING kids can hold in their hands to solve problems is helpful.
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Dice or Dot Cubes

Playing games with dice is just a fun way to practice subitizing (helping students easily recognize quantities without counting). These dot cube arrangements are helpful for so many strategies, one more, two more, doubles, etc.
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Give Visual Structure

Helping students put their visuals into a structure that helps them problem solve more easily is key. Dot cubes, ten frames, and five groups are great visuals that foster number sense development (click HERE for printable).

Building Number Sense at Home

The First Four Number Sense Relationships

"Number sense" is that good intuition about numbers and how they are related. This allows students to understand and use numbers in flexible ways. The beginning stages of number sense involve exploring four relationships:


  • Verbal counting (up to 10 in order)
  • Object counting (attaching a # to an item, 1:1 matching)
  • Cardinality (the last # counted tells how many in the set)
  • Subitizing (easily recognizing amounts without counting)

This is where much of our work in Kindergarten is done. These skills are critical and they do not develop overnight. We make sure to explore these numbers in a variety of ways and in many different contexts.

Spatial Relationships

Moving on and adding another layer to the first four number sense relationships, we look at spatial relationships. Spatial relationships help give a visual to a numeral. This also connects to our continuous work on subitizing. We talked about giving our visuals structure. Some of the structures that support students' work on spacial relationships are ten frames, dot cubes, and five groups. The Tiny Polka Dot game I will share with you is a great way to develop spatial relationships, looking at how numbers are composed or decomposed.
Tiny Polka Dot Print and Play
Here is a printable version of a game I love called Tiny Polka Dot. It is from Math for Love and it is a fun game that builds number sense.

1 & 2 More and Less

Once students have a solid foundation and a good understanding of the first four relationships, they are equipped to be flexible with their spatial relationships. The next number sense relationship that is extremely beneficial is knowing one more & two more and one less & two less than a given number without counting
The Progression of Early Number & Counting

Benchmarks of 5 and 10

Seeing how numbers relate to 5 and 10 is one of the most important number sense relationships children will build. We are a base-ten system, so ten is a powerful number. We also need to know that 2 fives make up a ten. Once students have built their early number sense relationships, they can then begin to see how numbers relate to 5 and 10. If you take 7 for example, we want students to know that 7 is 2 more than 5 and 3 less than 10. This is where the ten frame comes in handy, giving a visual to this thinking. We focus on how numbers relate to 10 often, but how numbers relate to 5 is just as important. As students move on to first and second grade, all of this knowledge can be translated into their work with larger numbers too: making the next ten, the next hundred, the next thousand, and so on. No whole number will ever be more than 2 away from benchmark number, making this a very powerful relationship.
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Number Rack

https://www.mathlearningcenter.org/apps/number-rack


Number Racks (also known as rekenreks) facilitate the natural development of children's number sense. In the Number Rack app, rows of movable, colored beads encourage learners to think in groups of 5s and 10s, helping them to explore and discover a variety of addition and subtraction strategies.

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Math Hands

When students are showing a number the "math way" they always begin with their left pinky and put up the next consecutive finger. This progression matches the number rack and it is a great visual to see that 5 (on one hand) and 1 (on one hand) makes 6; they can also see that 4 of their ten fingers are still down. We also call these "piano fingers" when we put them on the carpet to support developing these fine motor movements
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Building Visuals

If students work to build their visuals they will have a picture of 17 that might look like this. They know that 5 + 5 + 5 + 2 = 17 or 10 and 7 make 17. They can also see that 5 and 2 more is 7. They also see that 2 and 3 more fill that bottom row of the ten frame. They will know that 17 + 3 = 20 (2 full ten frames).

Part Part Total or Part Part Whole

As parents, this is the number sense relationship that we will probably feel most comfortable with. The idea that parts and a total are related makes sense to us, and it connect to the way we think about numbers. It is the basis for addition and subtraction. Teachers are now using more tools to help build visuals for this concept. We use picture bonds, where students can see the objects as pictures coming together to form the total or they can see the total being broken down into different parts. We use number bonds, a more abstract tool, where digits are used to illustrate the part part total relationship. The key in building this number sense relationship is to give students as many experiences using blocks, counters, linking cubes, etc. and then share their observations about how they put total towers together or how they broke apart their totals is key. Much of their understanding of the part part whole relationships connects to the important play activities they have been doing for many years.
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Picture Bond

This picture is one of the ways students begin to use number bonds. The students see that 3 red cubes and 5 blue cubes come together to make 8 cubes total. They can also draw pictures that would illustrate the same concept.
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Number Bond

Here is a number bond, it is a more abstract tool that students use to illustrate how parts and totals are related. 3 and 5 make 8, 5 and 3 make 8, 8 take out a part of 3 leaves a part of 5, or 8 take out a part of 5 leaves a part of 3.
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Putting it All Together

Above you can see the number bond and the part part whole number bond. Students could also make different ways of making 8 using their cubes. ( 1 + 7, 2 + 6)

Having a Mathematical Mindset

Growth Mindset

I love the illustration of the difference between a growth mindset and a fixed mindset below. Helping students develop their growth mindsets is a key element in teaching. We want students to know that they can train their brains to do new and seemingly difficult things. There is value in making mistakes as opportunities to learn and grow. Having a growth mindset helps students tackle any struggle that comes their way, academic or otherwise.

PLEASE SHARE ANY COMMENTS OR SUGGESTIONS.

Nell Hildebrand

Elementary Mathematics Instructional Coach

Rocklin Unified School District

nhildebrand@rocklinusd.org