In this lesson plan, your learner will explore counting from 0 to 100 on number lines, focusing on multiples of ten. They'll practice dual counting, identify numbers on a number line, and understand the concept of number length using bead strings. This interactive approach enhances their grasp of numbers within 100 and improves their counting efficiency.
Key Concepts for Exploring 0 to 100 on Number Lines
Here are a few concepts that are helpful to know for the lesson:
Crossing Multiples of Ten: Crossing multiples of ten, also known as "crossing the decades," can be challenging for learners, especially when counting numbers before and after multiples of ten, such as 39, 40, 41. Extra attention should be placed on counting the numbers just before and after multiples of ten to build fluency.
Number Lines with Larger Numbers: When working with number lines that include larger numbers, learners will rely more on using tick marks to recognize the positions of numbers since not all numbers are labeled. For example, on a number line where multiples of ten are labeled, the tick mark halfway between 20 and 30 represents 25.
Teaching Plan
The following activities will help your learner become confident with exploring numbers 0 to 100 on number lines. Be sure to work at a pace that is comfortable for your learner.
Examples and visuals to support the lesson:
1. Review Counting Within 100
Begin with a review of counting multiples of ten, then progress to counting by ones to 100. Use a variety of representations such as number lines, hundred squares, and Gattegno charts to support dual counting between 20 and 100, counting both forward and backward. For example, dual counting 21, 22, 23 could be "two-ten one, two-ten two, two-ten three" followed by "twenty-one, twenty-two, twenty-three."
Focus extra attention on counting forward and backward over the tens boundaries. If using a number line with only the multiples of ten marked, initially mark the numbers with nine ones (19, 29, 39, etc.) to support backward counting. The Gattegno chart is also useful for this purpose.
During counting, stop at regular points and ask your learner to identify 'one more' or 'one less'. Then provide missing number problems. Ensure your learner is fluent in identifying one more and one less over the tens boundaries as well as within each ten.
Skill Check
I can recognize and count numbers up to 100.
2. Locating Multiples of 10
Next, look at identifying the two multiples of ten which a given number sits between. Begin by identifying groups of numbers on the number line, asking, for example: "Where are the twenties numbers?" "Where are the fifties numbers?"
Start with a number line that only has multiples of ten labeled. Identify specific numbers on the number line and identify the previous and next multiples of ten. Then move on to number lines with all numbers labeled, and finally to numbers in isolation without the aid of a number line.
Encourage your learner to use the following stem sentences: "_ is between _ and _; _ is the previous multiple of ten; _ is the next multiple of ten." For example, "The number marked A is between thirty and forty; thirty is the previous multiple of ten; forty is the next multiple of ten."
Skill Check
I can find multiples of ten on a number line.
3. Identifying Numbers on the Number Line
Work towards identifying a number on the number line. First, spend some time looking at the layout of the number line in detail, noting how the multiples of ten are marked. Emphasize the tick marks in the middle of each section between multiples of ten (e.g., 15, 25) and the smaller tick marks indicating the ones.
Show a number line with a given number that is marked but not identified. Initially, show your learner how to look at the previous multiple of ten, modeling language such as "I know this is going to be a fifties number." Then count up from the previous multiple of ten, in ones, or apply knowledge of the zero to ten number line, to identify the number indicated.
Once your learner can easily find whole tens and numbers with five ones, look at numbers that can be identified as one more or one less than these numbers (e.g., 29, 31, 34, and 36). Then progress to two more or two less (e.g., 28, 32, 33, and 37). Practice identifying a range of marked numbers between 20 and 100, ensuring that you always use a number line with the tick marks for fives emphasized.
Skill Check
I can identify a number that is marked on a number line.
4. Placing Numbers on the Number Line
Now move on to placing a given number on a number line. For example, instruct your learner to place these numbers on the number line: 21, 29, 32, 38, 43, 72, 83, 94. Continue to use number lines with the tick marks for the fives emphasized.
Ensure your learner locates the previous multiple of ten and counts forward from there by ones. Eventually, they may use strategies such as locating 40 and knowing that 48 is 45 (the midpoint between 40 and 50) and three more, or locating 50 and knowing that 48 is two less than 50. Promote these strategies by verbalizing a similar thought process as you show how to place numbers on the number line.
If your learner counts in ones from the start of the number line, give additional support to use the previous multiple of ten as a starting point before counting up from there.
Skill Check
I can find the position of a number and write it on a number line.
5. Exploring Numbers as Length
Develop your learner’s understanding of number as length. Bead strings are a useful representation for making a link between number as quantity (e.g., 32 things, or three lots of ten things and two more), number as length (e.g., a length of 32 units), and the position of a number on the number line. Ideally, each group of ten beads would alternate colors so that your learner can see the groups of ten clearly.
Using a bead string (or an image of a bead string), ask how to use the colored groups of ten to find a given number of beads easily. If using a bead string, separate the beads; if using an image, circle the groups of beads. Here, focus on the group of 32 beads, not just the "number 32 bead."
Begin talking about length by drawing a line under an image of a bead string and asking, "How many beads long is this?" Draw lines of different lengths on the ground along with a 100-centimeter reference line. Show your learner a meter stick to demonstrate that the reference lines are 100 centimeters. Guide your learner in estimating lengths relative to 100 centimeters. Estimate the position of multiples of ten as a starting point, before refining the estimate down to the ones digit, for example:
"I know that fifty is in the middle of zero and one hundred. I think this line is a bit more than fifty. I think it is fifty-three centimeters long." "This is near one hundred. I think it is an eighties or nineties number. I think this line is about eighty-five centimeters long." Encourage your learner to verbalize their thinking in this way as they visit each line on the ground.
Estimation should be relative to the 100-centimeter reference line and should not involve actual measuring. Reasonable estimates should be celebrated for showing good proportional understanding, focusing on where two-digit numbers sit in the number system rather than the ability to manipulate and read a meter stick.
Skill Check
I can use what I know about the positions of numbers on number lines to estimate length.
Summary
By exploring 0 to 100 on number lines and understanding multiples of ten, your learner will develop a strong grasp of counting and place value. These foundational skills are essential for their future math success. Keep practicing these activities to reinforce their learning and boost their confidence in working with numbers.
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Skill Check