Mainstream kindergarten and first grade classrooms would not be complete without proudly displaying the alphabet and a number line on the wall. Often taped to the top of each student’s desk is a laminated number line that a student can easily access. Why do number lines have such a prominent place in classrooms? Number lines help to provide a mental strategy for addition and subtraction; research has shown that number lines are important because they promote good mental number sense and arithmetic strategies.
We all agree that number lines are important. So, how do we teach number number line concepts, especially to young students who are visually impaired? Best practice for students who are visually impaired supports the use of manipulatives to initially introduce basic math skills and number sense concepts. In Part 1 of this series, we will share a vareity of basic number line activities and follow a young student as he develops basic number sense through tactile number lines.
Jessica McDowell, a seasoned and creative TVI, has shared her materials and insight as she teaches number line concepts to this adorable first grade student. Logan is a braille reader and accesses his math in braille. Initially, Jessica introduced Logan to the standard APH tactile number lines (including the APH number line that ranges 0 to 20) along with smaller teacher-created number lines. His TVI pre-taught how to access a tactile number line and Logan followed his mainstream classroom as they learned to use number lines to learn foundational math concepts.
*Note: It is important that the tactile number lines are created with tick marks and with the number brailled below the tick mark. Braille students have to be taught to use tick marks (important for adding and subtracting) and how to physically drag a finger straight down to locate the number in braille.
The class did many games and activities on concepts without using the book or doing paper/pencil activities. Many of these games required modification to be accessible or substituted games were used.
Note: Many classrooms use motivating – but inaccessible – apps to practice number line skills.
Eventually, the students were assessed on paper and Logan did not have much time with textbook tactile graphics for number lines before the assessment.
Create fun interactive number line games to practice the basic number line skills including the ability to find the dot on the number line. Start with manipulatives such as creating a magnetic tactile number line and placing a fun shape/object magnetic on/just above the tick mark of the braille number line. Add a tactile number line to a cork board and have the student use a huge push pin on or slightly above the tick mark to label the desired number. (See the Number Line Activities post for the cork board activity and related number line activities.) As the student progresses, the student can place stickers (foam stickers work well!) on a teacher-created braille number line or the APH number line.
When introducing the number line, explain what the tick marks are and why they are used. Encourage the student to follow the tick marks to find the circle (or object) on the tick mark. Once the object is found, the student should drag his finger down the tick mark and continue down to find the the braille number that corresponds with that tick mark.
Encourage the student to identify the range of the number line and the scale. The range can be found by identifying the number on the far left and the number on the far right. Start with the scale of one – each number and tick mark increases by one. As the student progresses, the scale might change to increasing by twos, fives, tens or more.
Remember: The goal is to teach the student to follow the tick marks (not the braille numbers below the number line) to find the object; then, the student should drag his finger down to identify the correct number. (Reason: If a student is used to following the numbers instead of the tick marks, adding and subtracting becomes vary confusing as the student is then counting at the same time he is following braille numbers.)
Choose a simple number line (depending on the student, the range may be 1-5 or 1-10). Using one of the manipulative number lines mentioned above (magnetic board, cork board, etc.), ask the student to explore the tactile number line. Identify the various parts and the position/relationship of each part: tick marks, straight horizontal line, and numbers. Start on the left and move right. Students may need to follow the straight horizontal line first, before being able to follow the tick marks. Ask the student to start on the left side and count the tick marks (be sure to start with the same number – zero or one – that is in braille for this number line). Then, ask the student to read the braille numbers below the number line. Did his tick mark count match the braille numbers? Go back and recount the tick marks.
Now, quietly add a magnetic or push pin object slightly above a tick mark; never place the sticker on the braille number! (Initially chose a tick mark in the middle of the number line, so the student practices following and then counting the tick mark.) Encourage the student to identify the corresponding number by dragging his finger down to the braille number.
With the 10-frame below, first grader, Logan, moves Spot (a three dimensional ladybug along a 10-frame tray cut in half longways and made into 1×10 (instead of a 2×5). Jessica (TVI) added a row of corresponding braille numbers below the ten frame (each number aligned centered with each ten frame square). In the picture below, the corresponding braille numbers ranged from 1-10. Jessica made additional corresponding number lines such as 10 – 100 (counting by tens) that could easily be swapped out. At the bottom of the image is the APH 0-20 number line which is not as long as the 10-frame number line.
With the ladybug activity, Logan learned to count the squares as he identified the square that the ladybug was in.
The next step is to ask your student to find and place the marker on or slightly above the desired tick mark. When using the 1×10 frame, Logan learned to count the squares in order to place the ladybug in a desired square. Moving the ladybug while counting squares is more concrete than counting the tick marks. He also learned to find the braille number below the ten frame.
The timing of these number line activities will depend on the student’s age and ability. Some students may spend a week on each piece of an activity while other students may rapidly progress through many of these activities in one lesson. Keep in mind that most young students need time and practice – repeating the same activity or similar activities again and again before they are ready to move on to the next step. For students with vision, teachers typically have numerous games that provide multiple opportunities to repeat the same skill before moving on to the next skill.
Note: Introduce the basic number line concepts in the order that the mainstream classroom is introduced. Remember, the goal is for the general education teacher to take responsibility of teaching the student; the TVI’s responsibility is to modify materials and pre-teach concepts that are unique to students who are visually impaired and to support the general education teacher.
With each activity, maximun student independence is encouraged. Logan is expected to read his braille math problem independently, to announce the math problem aloud, announce as he counts, and to have a ‘plan’ on how to figure out the answer. He automatically moves his hands to his manipulatives and/or number line to figure out the problem. Very little prompting – if any – is given. Logan is allowed to make mistakes and if necessary receives additional instruction later to correct his mistake. After finding the answer, Logan is initially prompted to restate the math problem and answer. (In Part 2 of this series, Logan automatically restates the math problem and answer without prompting.) It is also interesting to note that Logan is able to sit still while working even though he has lots of energy when he is not physically interacting with the manipulatives or tactile materials.
Counting is a pre-requisite skill before introducing the “What’s Missing” activity. Filling in the blanks for a sequence of numbers and on a number grid is an activity and assessment question that is seen throughout early elementary grades. Students should also be able to read braille numbers. First create a simple braille page with the numbers 1-10 (leave two blank spaces between the numbers to give the student time to process the numbers he has just read) and ask the student to read the braille numbers. Next, give the student a simple braille page with numbers 1 – 10, with a number missing. (If necessary, initially, you can leave a blank space for the missing number to help prompt the student to independently identify the missing number.) Repeat the game with braille pages that have several missing numbers and/or different number ranges. Want a challenge? Vary the numbers by counting by twos, fives or tens!
In the follow video, Logan is given a teacher-created braille page with a range of numbers ending at 101; various numbers are missing. Using both hands, Logan sits quietly and reads the numbers across the page, identifying which numbers are missing.
Once the student understands the concept of identifying the missing numbers, give the student teacher-created number lines with missing numbers.
Note: With the missing number number line activity, the student will follow along the braille numbers and not the tick marks on the number line. However, be sure to point out to the student that for most number line activities – such as adding and subtracting – the student should count the tick marks, not the braille numbers.
Ask the student if the numbers “grow” (become larger) as you move to the right or to the left across the number line. Discuss the concept that the more you move to the right, the higher the number. If you move to the left (backwards on the number line) the numbers become smaller.
Use your desired manipulative number line; this example will use Logan’s 1×10-frame, 2 ladybugs, and 2 frogs. On three index cards, braille one of these math symbols: Greater Than, Equals or Less Than. Place a ladybug and the frog manipulatives in different squares; begin with the ladybug being larger than the frog. Discuss which number is larger, the ladybug or the frog? Introduce the corresponding Greater Than math symbol. Create a math equation by placing the second ladybug on an index card (leaving space for the math symbol card) and the second frog on another index card. Ask the student to place the Greater Than symbol between the two bugs. Repeat this activity multiple times with the Greater Than symbol. If the student is ready, substitute the second ladybug and frog with index cards that state the corresponding number. Example: If the ladybug is on 5 and the frog is on 2, an index card with the braille number 5 would be substituted for the ladybug and the index card with the braille number two would be substituted for the frog.
Introduce the process with the Less Than and then the Equals math symbols. Some students may benefit from simply choosing the correct math symbol and not creating the math equation.
APH has several tactile number line resources that you may find helpful:
This post is part of a series of Number Line posts.
By Diane Brauner