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Background

Tools are utilized every day by people to help them accomplish tasks and solve problems. This Number Line: Addition Unit will familiarize you and your students with specific tools that help solve addition equations. The tools that your students will use include a 123 Robot, a number line, and manipulatives. Students will also learn how to move their 123 Robot on a number line effectively to solve equations.

Number Line

A number line is a line of numbers marked at certain intervals or equal spaces with numbers placed in a particular order. The numbers ascend moving positively from zero and descend moving negatively from zero. It is a useful tool for adding and subtracting numbers. Moreover, the number line helps students visualize numbers while solving problems. The number line also helps represent a one-to-one correspondence. One-to-one correspondence is the ability to match one object to one (corresponding) number or object. Students will know one movement of the 123 Robot on the number line is equal to the number one being added in an equation.

number line

Counting Strategies

Students use a variety of counting strategies when beginning to learn addition and subtraction. This fact is captured in the following Common Core Math Standard for first grade: Relate Counting to addition and subtraction (e.g., by counting on 2 to add 2). This standard is the main focus of this STEM Lab. There are a variety of counting strategies for both addition and subtraction, including counting all, counting on, and counting back.

When students use the counting all strategy (for addition and subtraction), they start with 1 and count to find the total number of objects. For example, 7 + 2, the student would start counting from 1, count up to 7, and count up 2 more: 1, 2, 3, 4, 5, 6, 7...8, 9.

Another strategy students may use is the counting on strategy (for addition), students count from the start number rather than starting at 1. For example, 7 + 2, the students would start at 7...8, 9. However, using the counting on strategy (for subtraction), students start with the subtrahend number and count on to reach the total. For example, 12-5, the student would start with 5 and count up to 12 by ones: 5...6, 7, 8, 9, 10, 11, 12.
The last strategy mentioned above, counting back, happens when students are solving subtraction problems. Students using the counting back strategy will start with the total and then count back the number being subtracted. For example, 12-5, students will start with 5 and count up to 12 by ones, 5...6, 7, 8, 9, 10, 11, 12.

As you practice solving problems with your students, be aware of a common misconception with students regarding double counting. For example, if a student is adding 3 + 5, they may begin at 3 and end up with an answer of 7 rather than counting on from 3 and ending with the correct answer of 8.

It is very prevalent for students to use their fingers to count or help solve addition and subtraction equations. As students understand and use other counting strategies, students should be lightly discouraged from using their fingers when solving addition and subtraction equations. Supporting and providing practice as students develop an understanding of the counting strategies is encouraged to make connections to more sophisticated strategies in their future learning.

Manipulatives

Manipulatives are physical objects used in hands-on learning experiences to represent a concept. In this unit, crayons are the suggested manipulatives. Manipulatives are helpful to students when solving math equations because the students can visualize the numbers they are adding together. The manipulatives also support students in relating counting to addition and subtraction. Students will be asked to count the manipulatives in order to equal the same number as the sum of the addition problem during the activities. This is a great way for students to check their work to make sure the manipulatives match the answer to the equation which students get to do in Lab 2 Play Part 1 and Play Part 2.

One-to-One Correspondence

It is usually explained as the ability to match one object to one (corresponding) number or object.

  • Example: 1 button press on the 123 Robot = 1 movement
    robot button pressed
    1 button press
    robot movement right
    1 robot movement

Algorithm

Algorithms are a list of well-defined instructions made to solve a specific problem or perform a task. Algorithms typically reference computer-implementable instructions, but can include other instructions on how to brush your teeth or more complex tasks like operating a jet ski.

During this Unit, students will be following a set of instructions in a specific order to operate the 123 Robot. For more information about how to use the 123 Robot, see the Using the VEX 123 Robot Knowledge Base article. For information on how to code the 123 Robot using Touch buttons, see the Coding with the Touch Buttons on the 123 Robot Knowledge Base article.

The algorithm to move the 123 Robot is:

  1. Push to Wake
  2. Touch to Code
  3. Shake to Erase
Algorithm for 123 robot