In this lesson plan, your learner will use several hands-on activities and visual aids to practice identifying and writing multiples of 10 on number lines. We'll present a 0-100 number line alongside a set of linked cubes and a 0-10 number line to help your learner make connections between smaller units and larger multiples of ten. Then your learner will practicing using the number line to estimate the positions of numbers and compare their values.
Here are a few concepts that are helpful to know for the lesson:
Number Lines with Larger Numbers: As number lines extend to larger numbers, it isn't practical to label each individual number. Instead, intervals of numbers are labeled to maintain clarity and simplicity. For instance, on a number line from 0 to 100, multiples of ten are often marked to serve as primary reference points. Multiples of five can be recognized as halfway points between each multiple of ten.
Using Number Lines to Reinforce Math Concepts: Number lines are a powerful tool in helping learners grasp various mathematical concepts beyond just the counting order of numbers. A few of these concepts include distance, length, and proportionality. For example, learners can see that the distance between 0-50 is the same as the distance between 50-100.
Teaching Plan
The following activities will help your learner become confident in identifying and writing multiples of 10 on number lines. Remember to go at a pace that is comfortable for your learner.
Examples and visuals to support the lesson:
1. Review of Multiples of Ten
Start with a variety of tasks to help your learner review multiples of ten. Here are a few examples:
Provide your learner with sticks of ten cubes joined together and have them measure objects around the room. This will help them get a feel for the relative sizes of the numbers.
Show them a tower that represents a multiple of ten and ask, "What's the next multiple of ten? What's the previous multiple of ten?"
Encourage them to practice dual counting by saying the number as a multiple of ten and using the proper name (e.g. 3 tens and thirty).
After they've practiced counting and using the sticks of cubes, have your learner complete missing number sequences for the multiples of ten.
Skill Check
I can use multiples of 10 to measure objects and compare their sizes.
2. Exploring Number Lines up to 100
Next, introduce the 0-100 number line alongside a set of 10 multilink ten sticks and a 0-10 number line. Have your learner compare the two number lines, identifying the similarities and differences. Draw attention to the unit size of 1 on the 0-10 number line and the unit size of 10 on the 0-100 number line.
Once they understand the horizontal number lines, incorporate a variety of representations that show multiples of 10 in equal intervals. Vertical number lines, such as on a thermometer, can help them make connections to various contexts.
A Gattegno number chart is useful for showing connections between the numbers 1-9 and 10-90. Continue to practice dual counting while pointing to the numbers on the number line or Gattengno chart.
Skill Check
I can see that the pattern of 0-10 on a number line is similar to 0-100 on a number line.
3. Writing Multiples of Ten on Number Lines
Provide your learner with a variety of tasks that involve writing multiples of ten on number lines.
Begin with a 0-10 number line aligned with a 0-100 number line. Have your learner fill in missing numbers on the 0-100 number line. Then have them practice placing number cards on a blank 0-100 number line.
When working with a blank number line, encourage your learner to mark the midpoint before placing other numbers. On a 0-100 chart, they can mark 50 and use it as a reference for other numbers.
There is no need for the placements to be completely accurate. However, your learner should be able to make reasonable estimates and justify their decision. After each estimation, reveal a complete number line for your learner to check their estimation.
To provide further challenge, have your learner estimate the position of numbers on number lines that have different multiples of ten marked as reference points. For example, ask them where forty is on a number line that is only marked with zero and seventy.
Skill Check
I can estimate the positions of multiples of 10 on number lines.
4. Using Number Lines to Compare Numbers
Number lines provide an excellent opportunity for practicing number comparisons. Have your learner compare multiples of ten using the cardinality (size) and ordinality (relative position) of the numbers.
Begin with concrete objects such as sticks of ten cubes and progress to more abstract representations like number lines and inequality statements with symbols.
Here are a few examples:
Show a group of 3 ten sticks and 1 ten stick and ask which number is greater. Your learner may say, "three tens are greater than one ten" or "thirty is greater than ten."
Teddy says that forty is less than sixty. Is he right? Convince me using a number line.
Fill in each problem with the correct symbol (<, >, =): 6 tens ___ 8 tens; 40 ___ 7; tens; 90 ___ 80.
Skill Check
I can use number lines to compare multiples of 10.
5. Challenge Activities
If your learner is ready for an additional challenge, provide them with tasks such as these:
I'm thinking of a number. It is greater than twenty and less than six tens. What could it be?
Sarah and Deb have some ten-cent coins. Sarah has fewer coins than Deb. If Deb has fifty cents, how much money might Sarah have?
Have your learner create similar problems of their own for you to solve.
Summary
Understanding multiples of ten is a foundational skill that supports learners in their broader mathematical journey. Through hands-on activities, dual counting, and number line comparisons, learners develop a strong grasp of how multiples of ten function and relate to each other. They learn to make reasonable estimates, compare numbers using cardinality and ordinality, and solve practical problems involving multiples of ten.
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Skill Check