Base-Ten Hoppers
Est. Class Sessions: 2
Students use moves of ones and tens on number lines and 200 Charts to develop mental math skills and number sense. They develop flexibility composing and decomposing numbers.
Content in this Lesson
- Composing and decomposing numbers using ones and tens [E2].
- Skip counting by tens.
- Partitioning numbers into tens and ones using numbers lines and number sentences [E3].
- Recognizing that different partitions of a number have the same total [E7].
- Reading and writing numbers to the hundreds [E5].
- Making connections between place value concepts and representations of numbers with number lines and number sentences [E6].
- Solving addition and subtraction word problems involving two whole numbers using number lines [E8].
Daily Practice and Problems Q–T
Materials for Students
| Daily Practice and Problems | Lesson | Homework | Assessment | ||
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Student Book |
Student Activity Book |
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Teacher Resources |
Teacher Guide - digital |
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Supplies for Students
desk number line (0–100)
Materials for the Teacher
Display of Base-Ten Hoppers (Student Activity Book) Pages 251–254. See Materials Preparation.
Display of Open Number Lines Master (Teacher Guide)
Display of 200 Chart (Student Activity Book) Reference
Unit 5 Assessment Record
class number line (0–130)
Materials Preparation
Prepare Open Number Lines Master. Make several copies of the Open Number Lines Master. Students will use these to share their solutions and you will use it in Summarizing the Lesson.
Prepare Optional Targeted Practice. Make additional copies of the Open Number Lines Master. Add directions such as the ones listed below to provide extra practice with decomposing numbers into tens and ones. Sample directions:
- Start at 20 and move forward 19.
- Start at 25 and move backward 12.
- Start at 37 and move forward 35.
- Start at 55 and move backward 18.
- Start at 110 and move forward 26.
Content Note
This lesson provides a context for students to develop skills composing and decomposing numbers. Number lines serve as tools for developing mental images of numbers decomposed into groups of ones, tens, and hundreds. The goal is for students to develop mental math skills that will allow them to use flexible and efficient strategies to estimate, add, and subtract. They draw on their experience adding ten to a number on the 200 Chart. Then they transfer that experience to the number line which displays the same numbers in a visually different representation. For example, to add 43 and 39, students can think of moves on a 200 Chart that start at 43. Since 39 is 1 less than 40, they move forward 4 tens, and then back one: 43, 53, 63, 73, 83, and back one to 82. Knowing the moves on the 200 Chart helps students to represent them on the number line. See Figure 1.
Figure 1: 43 + 10 + 10 + 10 + 10 − 1 = 82
Other students may choose to start at 43, count on 7 until they get to the next ten (50), count on 3 tens (60, 70, 80), and then count on 2 more 81, 82. See Figure 2.
Figure 2: 43 + 7 + 10 + 10 + 10 + 1 + 1 = 82
Place the emphasis of this lesson on using the number line to break apart and combine numbers using hundreds, tens, and ones in flexible and efficient ways. Focus on supporting this kind of thinking rather than demanding precise notation. Students should learn to represent their moves on the number lines so that others can understand their thinking. However, developing consistent notation is not as important as developing flexible thinking.
Assessment in this Lesson
| Assessment | Expectation Assessed | Math Practices Expectation Assessed |
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Base-Ten Hoppers Check-In: Questions I–K Student Activity Book Pages 253–254 |
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