Understanding Making Ten In Mathematics
“Making ten” is a key strategy in early mathematics that strengthens students’ understanding of number relationships within the base-ten system. Because ten is a fundamental benchmark in our number system, recognizing how numbers pair to make ten helps simplify calculations and supports a deeper grasp of place value.
Mastering the concept of making ten allows students to think flexibly about numbers. For example, if a student knows that 9 + 7 can be thought of as 10 + 6, they are leveraging the structure of ten to simplify the problem. This skill supports mental math fluency, promotes efficient strategies, and sets the stage for understanding more complex computations.
Teaching Strategies For Making Ten
Using Visuals and Manipulatives to Teach Making Ten
Ten frames are one of the most effective tools for helping students visualize the concept of making ten. Organizing counters in a ten frame is a way for students to see how numbers decompose and recombine to form ten.
As students progress, double ten frames can reinforce how numbers group into tens and support larger sums. For example, to solve 9 + 7, students can place 9 counters on a double ten frame. They’ll notice that adding 1 counter completes one frame, leaving 6 counters to fill the second frame. This gives them 10 + 6 = 16.
Other manipulatives like Unifix cubes or counters grouped into ten can also provide hands-on ways for students to explore making ten. Allow students to build groups of ten physically by combining smaller groups. For example, present 8 cubes and ask how many more are needed to make a group of ten. Students can physically add 2 more cubes to complete the group.
The rekenrek allows students to slide beads to make groups of ten, providing a visual and tactile way to understand how numbers combine:
Using Making Ten to Transition to Mental Strategies
Once students are comfortable with physical tools like ten frames, they can move to mental strategies for making ten:
- Counting On: Encourage students to start at the larger number and “count up” to ten, then add what is left. For 8 + 4, students recognize 8 + 2 = 10, and then add the remaining 2 to get 12. This strategy builds fluency and reinforces the role of ten as a benchmark.
- Number Bonds: Use number bonds to demonstrate how numbers can be broken into parts to make ten. For instance, 9 + 6 becomes 9 + 1 + 5, where 9+1 makes 10, and 5 completes the sum. This flexible thinking develops deeper number sense and supports problem-solving efficiency.
- Number Line Visualizations: Using an open number line can help students understand how to “jump” to ten. For example, solving 8+5 on a number line involves a jump of 2 to make ten, followed by a jump of 3 to reach 13. Number lines make this process visible and reinforce the idea of building toward benchmarks.
Connecting Making Ten to Real-World Contexts
The making ten strategy is particularly useful for financial literacy. For instance, if a student has 65 cents and wants to make a dollar, they can calculate how many more cents are needed by making ten: 65 + 5 = 70, then 70 + 30 = 100. This reinforces the connection between making ten and real-world problem-solving.
Making ten is also relevant in measurement. For example, students might combine 7 centimeters and 3 centimeters to make 10 centimeters, reinforcing the concept of grouping smaller units into tens. Similarly, time calculations often involve grouping minutes into tens and then converting them into larger units like hours.
Building Number Sense Through Making Ten
Strengthening Connections Between Numbers With Making Ten
Making ten teaches students to see numbers as flexible and composed of parts. Solving 14 + 6 by thinking of 6 as 4 + 2, for example, reinforces the relationship between addition and decomposition. This strengthens students’ ability to approach problems in flexible ways.
Reinforcing Patterns in Numbers With Making Ten
Encourage students to practice making ten across various contexts. Start with visual tools like ten frames and gradually move to abstract problems. The repetition reinforces their ability to decompose and recompose numbers quickly and accurately.
Using Making Ten For Mental Math And Estimation
Making ten extends to estimation, a useful skill when solving real-world problems. For example, when estimating 58 + 47, students might round 58 to 60 and 47 to 50, then add 60 + 50 = 110. Adjustments can be made for greater accuracy, but the strategy remains rooted in grouping toward benchmarks like ten/multiples of ten.
Extending Making Ten to Larger Numbers
Once students master making ten with single-digit numbers, they can use it as a stepping stone for other problems, like making 100 or for subtraction.
For example, in 93 + 8, students can think of 8 as 7 + 1, calculate 93 + 7 = 100, and then add 1 to get 101.
In subtraction, 52 − 9 can be thought of as 52 − 10 = 42, then adding back 1 to get 43.
These strategies help students build confidence with larger numbers and prepare them for advanced mathematical operations, such as regrouping in multi-digit subtraction or mental estimation in multiplication and division.
Common Misconceptions About Making Ten
When teaching “making ten,” be mindful of common challenges:
Students may try to use making ten in situations where it’s inefficient or unnecessary, such as 50 + 25. This suggests they may see “making ten” as a rule to follow rather than a flexible strategy to use when helpful. Encouraging students to reflect on when and why a strategy is useful can support more strategic thinking.
Another common misconception is that some students may misapply decomposition by breaking apart numbers in ways that don’t support the making ten strategy. For example, they may rewrite 9 + 6 as 9 + 4 + 2 instead of 10 + 5. This suggests they may understand decomposition but not how to use it strategically. Visual models and guided examples can help reinforce purposeful number choices.
