Down Under 10 Strategy - Using it to Build Math Fluency
- Cheryl Fricchione
- 3 days ago
- 4 min read
In last week’s post in the Beyond the Algorithm series, we explored how students use the Make a Ten strategy to simplify addition problems by creating benchmark numbers that are easier to work with mentally.
This week, we’re looking at a closely related subtraction strategy often called the Down Under 10 strategy. Together, these strategies are part of a broader group of reasoning strategies built around making 10 as a benchmark number to simplify computation mentally.
When adults see students solve a problem like:
13 − 4
using multiple steps instead of subtracting 4 all at once, they often think students are doing more work than necessary.
But students using the Down Under 10 strategy are doing something mathematically important.
Rather than viewing subtraction as a single procedure, students are learning to use benchmark numbers and number relationships to simplify problems mentally.
What Is the Down Under 10 Strategy?
The Down Under 10 strategy helps students simplify subtraction problems by first subtracting enough to reach a benchmark number like 10.
Students decompose the amount being subtracted into smaller parts to make the problem easier to solve mentally.
For example:
13 − 4
A student may think:
subtract 3 to get to 10
subtract 1 more
10 − 1 = 9
This can be represented as:
13 − 3 − 1 = 9
Rather than counting backward one number at a time, students are using number relationships to simplify the problem.
Why Students Subtract Through 10
Ten is a benchmark number that is easier for many students to work with mentally.
When students first subtract enough to reach 10, the remaining subtraction is often easier to keep track of.
For example, many students may find:
10 − 2
easier to think about mentally than:
12 − 4
The strategy helps students use benchmark numbers to make subtraction problems easier to reason about mentally.
Over time, students begin recognizing how numbers can be decomposed and recomposed flexibly to make subtraction more manageable.
Finding the Difference Is About Reasoning, Not Steps
Just because students learn a new strategy does not mean they have to use it exclusively.
Learning more strategies gives students more options
However, it is important to note that young learners do not necessarily need to formally memorize or name every strategy as much as they need opportunities to reason flexibly about numbers and use approaches that make sense to them.
For example, in the problem:
14 − 6
students do not all need to think about subtraction in the exact same way.
One student may think:
subtract 4 to get to 10
subtract 2 more
10 − 2 = 8
Another student may think about the related addition facts instead:
6 + 4 = 10
10 + 4 = 14
so a total of 8 was added to get from 6 to 14.
This type of thinking connects directly to Grade 1 standard 1.OA.B.4, where students begin understanding subtraction as an unknown-addend problem.
Now that students have explored both Make a Ten and Down Under 10 strategies, they have multiple ways to reason about the same problem.
Some students may think about subtraction by taking away, while others may think about finding the missing amount through addition. In both cases, students are using benchmark numbers and relationships between numbers to make the mathematics easier to think about mentally.
For many Kindergarten and Grade 1 students, number paths are often more developmentally appropriate than traditional number lines because the spaces help students focus on counting quantities rather than distances between points. Number paths can help make students’ thinking visible as they learn to reason about benchmark numbers, addition, and subtraction.
I often use and recommend these Number Paths from EAI Education during fluency and strategy work with young learners.
This flexibility becomes increasingly important as students work with larger numbers, mental math, and multi-digit computation later on.
The goal is flexibility and sense-making, not memorizing a script or always solving problems one specific way.
The Importance of Knowing Number Pairs
Strategies like Make a Ten and Down Under 10 are built on students developing a strong understanding of the different combinations that make each number.
For example, students who know:
8 can be decomposed into 5 and 3
9 can be decomposed into 4 and 5
10 can be decomposed into many different combinations
are often better prepared to use flexible mental math strategies later on.
This work begins long before students formally use strategies like Make a Ten and Down Under 10 in Grade 1.
In Kindergarten, students develop fluency with decomposing numbers into parts through experiences with ten frames, counters, drawings, equations, and visual models. Over time, students begin recognizing that numbers can be broken apart and recombined in multiple ways while still representing the same total.
That understanding becomes an important foundation for later reasoning strategies.
One example of this early decomposition work can be seen in this Tuesday Try-It activity focused on decomposing numbers into two parts. You are welcome to download it and give it a try.
Families and educators can also support this work through simple games that encourage flexible thinking about numbers. One favorite is Shut the Box, which gives students repeated opportunities to think about combinations of numbers in meaningful and engaging ways.
If you enjoy exploring the mathematical reasoning behind the strategies students use in today’s classrooms, you can subscribe to the Tuesday Try-It Series for additional weekly mathematics activities, instructional ideas, and future posts in the Beyond the Algorithm series.
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