Walden Math Connection
Welcome! This new page is dedicated to Bridges in Mathematics, Walden’s math program. Here, you’ll find information about the curriculum along with tips and tools to help strengthen the connection between school and home for our young mathematicians.
We’re beginning with resources for our K/1 learners and will continue to build out the page over time. Please check back for updates!
Letter for K/1 Families from Math Specialist Youngin Kim
Dear Families,
In our K/1 classrooms, we use a variety of hands-on tools to support your child’s mathematical development. One of the most effective tools we use is the Number Rack—a simple but powerful tool that helps children build a strong foundation in number sense, counting, and basic arithmetic! We want to take a moment to explain how the Number Rack works, why it's so beneficial, and how you can use it at home to support your child's learning.
What is the Number Rack?
The Number Rack, also known as Rekenrek, is a fun and effective math tool that originated from the Netherlands that makes counting and calculations more visual and tactile. It may remind you of an abacus, but what makes the Number Rack unique is its use of color! You’ll notice that each of the two rows have 10 contrasting beads – 5 white and 5 red. This color distinction is a visual cue that helps young learners connect to the logic of our base-ten number system. It’s not just about counting in ones; the colors encourage children to think more flexibly and in groups of 5 and 10—a key milestone in developing strong number sense.
Why is it so effective?
Research shows that visual and tactile learning play a critical role in helping young children develop a strong and flexible number sense. Educators like Cathy Fosnot, who champion constructivist mathematics, emphasize how hands-on tools like the Number Rack help children connect abstract mathematical concepts to the real world. By actively manipulating objects, visualizing quantities, and exploring different ways of solving problems, children build their understanding of math in a way that feels meaningful and concrete (Fosnot and Dolk, 2001).
One of the most powerful features of the Number Rack is the way in which it visually facilitates the progression from 1-to-1 correspondence (counting each bead one by one) to a higher-level skill called subitizing. Subitizing is the ability to instantly recognize the number of objects in a group without having to count them, and research shows that it’s a strong predictor of a child’s number sense development.
For example, when a child is shown a set of beads representing the number 7, instead of counting each bead one by one, they can recognize that there are 5 beads, and then simply count on 6 and 7. This shift is key for developing efficient math strategies: this is the moment when they move from 1-to-1 counting to “counting on,” a huge step toward automaticity! They start to understand that 5 + 2 = 7 without having to recount everything.
The Number Rack’s visual structure supports this transition to more efficient, flexible, and automatic strategies for adding and subtracting. It helps children build a solid foundation in math, one that will serve them well as they grow into confident, powerful math thinkers!
How does it support learning?
When using the Number Rack, children engage in activities such as:
- Counting On/Subitizing: Counting beads in groups of 5 or 10 supports the development of skip counting and place value.
- Subtraction and Addition: Moving beads in and out of groups helps children visualize how numbers increase and decrease. For example, adding a bead means increasing the total, while taking a bead away shows subtraction.
- Number Relationships: Students can explore different ways to combine numbers and part-whole relationships (e.g., how to make 10, or 6 + 4 = 10).
- Visualizing Place Value: The Number Rack helps children understand the importance of tens and ones, an essential concept as they begin to work with larger numbers.
The Number Rack is a versatile and engaging tool that enhances early math skills in a hands-on way. It helps children visualize number relationships, improve their counting abilities, and build a strong number sense. By using it at school and continuing these activities at home, your child will develop a stickier understanding of math concepts.
Thank you for your support in reinforcing these important skills at home!
Warmly,
Youngin Kim
Walden Math Specialist
"When students see mathematics as a set of relationships between numbers, rather than just rules to memorize, they understand it more deeply. Manipulatives and visual tools, like the rekenrek and number lines, help students build these relationships and move beyond rote memorization."
— Jo Boaler, Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages, and Innovative Teaching (2016)
Number Rack Slide Deck Recording
Get to know the lingo!
Here are some terms you might have heard your child’s teacher say.
Number Sense: The ability to understand and work with numbers, recognizing patterns, comparing quantities, and grasping basic math concepts like addition and subtraction.
One-to-one correspondence: The ability to match each object with one number as you count, helping children understand that each object represents one unit. This is a crucial foundational skill that needs to be in place before more efficient counting strategies can be internalized.
Subitizing: The ability to instantly recognize the number of objects in a group without counting them one by one, such as seeing 4 beads and knowing there are 4 right away.