This is the fifth post in a series of how to successfully teach 21st Century classroom skills by pairing tactile graphics with digital resources. In this post, we will discuss using a tactile overlay on the iPad (app also available in Google Play!) to introduce the spatial layouts of adding and subtracting with carrying and regrouping. Adding and subtracting requires that students be able to apply tech skills such as being able to drag in a straight line across rows and down columns in order to add/subtract the correct numbers. Understanding the spatial layout is also critical, especially when carrying or regrouping is involved. Please see the previous posts in this series as they provide foundation skills that lead to solving digital math equations.
The Math Melodies app has a series of progress math-related games. The Math Melodies Addition and Subtraction games are the first digital math app that has created an accessible way to regroup and carry within the app. In this video tutorial, Jessica demonstrates the Math Melodies Addition equations under the First Grade Advanced level. These addition problems are laid out as vertical equations, most of which require carrying. The First Grade Advanced Subtraction problems are also laid out as vertical equations, most of which require regrouping.
Prior to solving these equations, students should be familiar with 0-9 math facts, should understand ones, tens and hundreds columns, and should have experience in dragging a finger up/down a column in a straight line.
Note: The First Grade Base level has 1-digit equations (ones column with simply carrying). While the First Grade Advanced equations have 2-digit addition problems (ones and tens columns). In the video tutorial, Jessica demonstrates the First Grade Advanced level in order to show how to solve equations that may be slightly more complex.
Pre-Teach the Spatial Layout
Review the braille version of a similar addition problem; discuss the ones and tens columns, where the answer goes (at the bottom of the equation) and where the carrying number is placed (at the top of the number). Think about having blank boxes to indicate where you input the answers and carrying numbers.
For some students, Pre-teaching the skills using the tactile graphic (before placing the graphic on the iPad) is preferred. Typically, this method is used with students who are distracted by VoiceOver speaking or who cannot keep their hands still. For most students, introducing the tactile overlay on the iPad is preferred, as VoiceOver provides verbal information as to what the student is touching. For many students, having the built-in verbal information available when using the digital addition and subtraction problems - especially when paired with the tactile overlays - increases the student's success in solving the equations and builds solid spatial concepts required for more complex math problems.
Initially focus on learning the spatial layout of the entire page using the tactile graphic. The tactile graphic has empty boxes for the equation, carrying, and answers "equals". It also has the smaller boxes with brailled answer choices along the bottom of the page and symbols for the buttons down the right side of the page. The buttons are the Back button, Quit button (quit this game) and Listen button (Read Aloud option for students who are not using VoiceOver). Have the student systematically explore the entire tactile graphic for the digital equation. What is different between the braille version and the tactile overlay graphic? How many rows of empty boxes are there and why? Where do you input your answer? Drag your finger down the ones column. Drag your finger down the tens column. Note: The app calls the top row of boxes the "carry" boxes and the bottom row of boxes the "equals" boxes. Note: The tactile overlay has bolder lines around the "carry" boxes and "answer" boxes, to indicate that you can input numbers in these boxes.
If pre-teaching, verbally say an equation. (Example: 65 + 8). Ask the student to repeat the equation. If introducing the tactile graphic on the iPad, confirm the numbers in the math problem by touching the very top of the screen (VoiceOver will announce the equation again.) Where does the first number go in the empty boxes? Where does the second number go? Find these numbers in the actual equation.
If your student has a good mental image of the equation, ask him/her what he/she will find if he/she drags his/her finger down the ones column? (Example: The student should remember or learning to build the mental image: 5, 8, "equals" box). Repeat with the tens columns - what will you find? Then confirm by dragging your finger down the tens column. (Example: The student should remember or learning to build the mental image: "carry" box, 6, blank, "equals" box.)
Teacher's Note: It is strongly recommended that the student drag around the screen and not right/left swipe. Right or left swipes will move through the boxes from left to right. Up or down swipe will NOT move up or down a column! (Up or down swipe will change whatever the rotor is set on.) When dragging, use a split tap to activate an "equals" box, carrying box or answer box.
Note: In the app, the smaller answer boxes do not appear until you split tap on an "equals" box. Navigate to the desired answer and split tap to select the desired answer. The answer will automatically be added to the selected "equals" box.
When a new page opens with a new equation, VoiceOver announces the math problem. Example: In the video tutorial, the first problem is announced, "How much is 73 + 6?" This is key information! The student should instantly develop a mental image of this equation, remember the numbers, and refer back to this mental image while solving the problem! In his/her mind, the student should visualize the vertical equation, lining up the "3" and "6" in the ones column and the "7" in the tens column.
After listening to VoiceOver announcing the equation and developing the mental image of the vertical equation, the student can confirm the numbers if desired or he/she can search for the ones column and start solving the equation. The student can confirm by dragging down from top, center of the screen to find the first number (in the photo below, the equation is 54 + 96; with 5 in the tens column), then drag right to find the ones column (in this case the 4). Some students do initially need to confirm the spatial layout by touching each individual number in the equation. However, this is not as efficient as simply touching the equation at the top of the page. If the student only needs to confirm the numbers in the problem - not the spatial layout - the student can touch the top of the screen to hear VoiceOver announce the full equation again.
Teacher's Note: Ask the student to say the equation before touching the screen! If the student is struggling to solve the equation, ask him/her periodically to say the equation and the steps as he/she solves the equation. Saying the equation is basically helping the student to think aloud, which helps not only the student process the steps, but also provides the teacher insights to the student's thinking process. When introducing this app, often it is helpful to model the thinking process by having you - the teacher - say the steps out loud when either modeling the process of solving the equation or when guiding/introducing the student through the process the first time.
Solving the Addition Problem
Once the student has the equation firmly in his/her mind, solve the equation by:
- Find the ones column (drag your finger down from the top - starting slightly right of center) looking for the specific number. (In the example 54 + 96, the number 4.)
- Drag down to find the number to be added to the 4. (In this case, the number 6.)
Drag down again to find the "equals" box in the ones column and split tap. This brings up the smaller answer boxes at the bottom of the screen.
- Drag to the desired number and split tap. (in this case the answer is 9.) The answer is automatically placed in the ones column "equals" box.
If the answer required carrying:
- Drag up to the find the "carry" box above the tens row (which in this case will be the "carry" box above have the number 5.)
- Split tap on the "carry" box (which opens the answer choices at the bottom of the screen).
- Find the desired number in the answer boxes at the bottom of the page and split tap. (In this example, the number 1). The answer is automatically placed in the "carry" box above the tens column.
Repeats steps as needed to add the tens column and then hundreds column.
In the video below, Jessica demonstrates how to use the tactile overlay with an addition problem and a subtraction problem in the Math Melody app. In this demonstration she includes how to carry and how to borrow/regroup.
Editor's Note: The process of carrying and borrowing sounds more complicated than it is! When solving the problem in braille, the student has to roll the paper up and down in the braille writer and line up the brailler embosser head in order to place the carried number or regrouped number above the equation. With the digital format, the student simply drags his finger to the desired box and split taps, then selects the desired answer from choices at the bottom of the page.
Editor's Note: In the video, Jessica demonstrated subtraction regrouping in the ones column and completing the ones answer before she crossed out ("slash" as the app calls it) the tens column. Often the order is to cross out the tens, add the new number in the "carry" box above the crossed out number, then change the ones number by adding the original number in the ones "carry "box, then select "Add ten" answer choice button. (Example: In the video example, 63 - 15, 6 is crossed out to make 5 and the 3 becomes 13.)
When introducing the subtraction problems in the Math Melodies app, follow the same strategies listed above for introducing the addition problems. Be sure to compare the braille format with the tactile overlay on the iPad! Instead of "carry" box above the tens column, there are now "regroup" boxes above the tens and the ones column. The first number in the tens column also has the option of "slash on" which means that the number has been borrowed from.
After the student is familiar with the tactile overlay, the spatial layout, then solve the problem. In the picture below, the equation is 63 - 15. You cannot take 5 away from 3, so you must borrow 10 from the number in the tens column.
When regrouping, find the number in the tens column that you will borrow 10 from.
- Cross out the 6 in the tens columns by split tapping on it. (The app calls this "slash on" as a slash mark is placed over the 6. VoiceOver then announces the number (6) "borrowed".
- Add the new tens number above the borrowed number. (In this case, you borrowed ten from the number 6, so place a 5 in "regroup" box at the top of the tens column. VoiceOver now announces the number (5) "regrouped".
Now move to the ones column and add ten to the original number. (In this example you will be adding 13 to the "regroup" box above the ones column.
- Drag to the "regroup" box above the ones and split tap.
- Drag to the desired answer choice at the bottom of the screen and split tap. (In this case 3.)
Add ten to the number 3 by dragging back to the "regroup" box above the ones and split tap.
- Drag to the Add Ten answer choice at the bottom of the screen and split tap. (Now the number 13 is in the regroup box above the ones column.)
- Hear the new ones column subtraction problem by dragging down the ones column, starting at the regroup box. (In this case, 13 - 5, "equals" box.
Add your ones column answer: When on the ones column "equals" box, split tap.
- Drag to the desired answer choice and split tap. (In this case, the answer choice is 8.)
- Repeat steps as needed for the tens column.
- Check your answer by selecting the "check answer" button now located at the bottom edge of the screen in the center. (Note: The tactile overlay does not show the check answer button as the answer number choice boxes cover the check answer button.
Tactile Overlays for Addition and Subtraction
A big thank you to Transcribing Mariners who have donated the embossable graphics work for the Paths to Technology Resource Library and this blog post. A huge thank you to Jessica McDowell, TVI extraordinaire, for sharing her work on bridging the gap between tactile graphics and digital resources!
- Addition Advanced Overlay pdf for PIAF/Swell
- Addition Advanced overlay docx for embosser
- Subtraction Advanced Overly pdf for PIAF/Swell
- Subtraction Advanced overlay docx for embosser
Related Posts Resources
- Tactile to Digital Part 1: Math Robot (Overview of the critical tech concepts unique to students who are blind or low vision and how to use APH's Math Robot app to teach these critical tech skills)
- Tactile to Digital Part 2: Math Melodies (Introduced the progression of using models, tactile graphics and iPad overlays to teach teach critical tech skills, including dragging in a straight line and applying grid concepts to the digital environment using the Math Melodies game, Add or Delete)
- Tactile Digital Part 3: Creating a Tactle Overlay on the Go! (Shared two quick and easy methods to created simple tactile overlays without an embosser or PIAF/Swell graphics machine)
- Tactile to Digital Part 4: Positions in a Table (Using a tactile overlay on the iPad to introduce the spatial layout of a table)
- Math Melodies in the App Store
- Math Melodies in Google Play Store
- Math Melodies App: Young Students Post
- Math Melodies App Part 1: Addition (Detailed video tutorials on how to solve digital math addition equations using VoiceOver)