Graph paper is beneficial for all math students!


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When you are shopping for school supplies, think about an extra journal or package of three ring binder paper: quad lined paper is the first and most economical help for your struggling Math student. A small minority of students gets visually confused by the squares on the page. So it is always best to search for paper that is very lightly printed with ‘unobtrusive’ squares: the emphasis should be on what your student is writing and drawing not on the grid. 

Neatly lining up calculations prevents errors. Quad paper can also help illustrate many concepts that are more complicated to explain in words but are easily seen on paper, such as multiplication, area and perimeter, for making graphs, and drawing congruent shapes, when showing transformations in size, slides, flips, and rotations and many more. 

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Dyscalculia often combined with ADHD, dyslexia, and dysgraphia


1. ADHD 

Many students with dyscalculia or Math LD also have ADD / ADHD.

In fact, new research mentions that inattentiveness is likely one of the underlying conditions in developing dyscalculia.
So it makes sense to implement the usual strategies that teachers know to be effective for ADD / ADHD to make sure your student(s) with math difficulties and dyscalculia can benefit the most of your lessons.

Minimizing distractions, the students’ location in the classroom, a quiet spot for individual work, a short interval between doing the math work and getting feedback, a clear method for self monitoring of being on task, a token reward system, and frequent breaks with some movement can all contribute to success.

2. Dyslexia

Students with dyslexia struggle to learn to read, their reading is slow and/or has a lot of errors and comprehension is often lacking. Most dyslexic children have a hard time with spelling. Contrary to general belief dyslexia does not start at the age of learning to read, but dyslexic children are born with a different brain structure and function. This hampers phonological awareness, the processing of single sounds that make up words. Recognizing rhyme, blending and segmenting words and syllables into single sounds is really hard for them. This ability is one of the precursors for learning to read and spell. Screening in KG and 1st grade will open the opportunity for early detection and intervention. Intensive structured phonics methods make the most effective intervention.

Dyslexia and dyscalculia are often combined (some articles mention in up to 30%). It is important to remediate the reading in order to be successful in math, in particular when doing word problems.

3. Dysgraphia

Dysgraphia is tied in with visuo-spatial abilities, one of the cornerstones in learning math. So it is to be expect that many dysgraphic students are struggling with math. It is obvious they need extra time for any written math work and for tests.

Using a tablet/laptop can be a blessing in language classes, but typing number sentences and formulas is cumbersome. Graph paper can help students with handwriting problems: each numeral and sign goes in a separate square and becomes more legible. Calculations are aligned and you can quickly spot an error and offer a targeted explanation.

Multiple Choice tests / quizzes do not ask for a written response so students can more easily show their math achievements. Please remember to provide square paper on the side to prevent the student being forced to scribble in the irregular shaped margins that are left open between the mc-questions.

Number-line Addition and Subtraction


Feel free to download our template “Addition and Subtraction on the number-line”, it provides and easy and playful way to teach Second graders and those at that learning level, to visualize Adding and Subtracting numbers.

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Take a quick guess before you count


Taking a quick guess before starting to count will help children get a ‘sense for quantity’.

Guessing the quantity of a few loosely scattered items or in a small heap and comparing quantities in two heaps are important precursors of later formal Math learning. The instantaneous perception of a quantity (subitizing) is particularly difficult for children with dyscalculia so you need to allow time and just stick with it. Don’t be surprised that in the beginning the guesses will be far off, like double and triple or less than half the actual amount of items.

For this fun activity you will need:

  • the printed download
  • a dozen colored counting bears, scrabble tiles, poker chips, or the like as counters.

Before the activity starts:

1. Fold the paper in half so you see only one row of leaves. Ask your child to touch each leave with a finger of one hand (the dominant hand preferably): so it is clear that one row is five leaves.

2. When you have played the game numerous times, you can unfold the paper and use two rows. Again have your child touch the leaves with each finger of both hands, so it is clear there are ten leaves.

3. Make sure your child knows the difference between quickly guessing or (giving an impression of the approximate number in the wink of an eye: it’s your child’s estimate, so it cannot be ‘wrong’) and actual counting.

Here’s the activity: guessing a quantity

Make a little unorganized heap of counters next to the paper (less than five items, you can increase the numbers later)

Ask your child to look at the heap only for a moment and guess the number before counting them. You can also cover them and only remove the cover for an instant to prevent the habit of starting to count them) 

Acknowledge any reasonable estimate without commenting and ask her to count by putting the items one by one on the leafs on the paper.

Your verbal encouragement could be something along the line of: “Wasn’t that fun? This time you guessed a number that was smaller than the counted number and last time a larger number, that’s both O.K., let’s play again.” 

In a later stage, when you are using the unfolded paper, your child will probably start to arrange the counters in manageable smaller heaps on the table before transferring them to the leaves.

Even better for Math development is arranging the counters into small geometric patterns like a line of two, a triangle of three, or a square of four. This will help to get a ‘feel’ for the number, like instantaneously ‘seeing’ a number, a bit like perceiving the three or four items together as a whole. Perceiving this ‘three-ness’ or ‘four-ness’ is called subitizing. 

The next level: comparing two quantities

 

Make two heaps of counters on either side of the printed download and ask for a quick guess which heap has the most items and use the paper to check. Do quickly guessing what is the smallest quantity for a change. You can easily make this into a fun game too.

 

Remember to keep it a game-like and fun activity and enjoy pre-Math!

  • Download our free template about Guessing as a strategy before starting to count:    {nicedownloads:5}

Instant Fix


Graph paper works wonders both for calculations and understanding concepts

Although there is no instant fix for dyscalculia, there is an instant fix to maximize your credits for the math you can do! Using graph paper (quad paper, quadrille paper) will help you both with calculations and understanding concepts! It can benefit applying concepts as well as communicating your thoughts about the math problem.

Making your own drawing to represent the question makes it more fun and clarifies all types of math work, you can also add colors to your work!

Initially using graph paper might take a few minutes more, but it will save you time in the long run as well as increase your grade.

Starting in KG

Having a square to write in will make learning to form the numerals easier. KinderGartners and 1st graders need larger squares and should be taught to leave an empty square between each numeral and between lines to prevent the numerals ‘bleed into each other’.

Elementary

Depending upon fine motor skills / penmanship and the progress in math, somewhat smaller size squares will come in handy now.

Using graph paper makes it quick and easy to draw a number-line and to show your additions and subtractions as ‘jumps’, including the multiples of ten numbers as ‘stepping stones’. It can also easily illustrate multiplication as repeated addition and division as repeated subtraction. Extending the number-line to the left from zero later explains negative numbers.

Using the sides of the squares as a guide for drawing will enable you to easily visualize and compare areas and perimeters and help you solve problems about area and perimeter.

Writing each numeral in it’s own square will help you to keep the    digits in multiplications and long divisions aligned, so you do not mix up your units, tens, and hundreds, etc.

The grid will help you find lines of symmetry, complete symmetry drawings (like our free download activity) and make artistic patterns. When you cut out shapes or fold and cut the sides of a large square to make a star or snowflake, the printed squares will help you make strait cuts or folds. These activities are enhancing visual-spatial abilities, one of the components that contribute to being a mathematician.

Grid paper helps you to make the link between manipulatives and drawing models. By drawing a model the student shows he has internalized the concept that was illustrated by using manipulatives. The model shows his/her thinking and helps the teacher/tutor/parent to see if there are any remaining misconceptions, and if so which help is needed.

Middle and High school

Together with switching from wide ruled to college ruled paper you will now probably go for the small squares, allowing for more complex algebraic equations and working with geometric shapes.

In algebra it will keep those little ‘devilish’ minuses and other small math signs like powers etc. securely locked in your equations.

When you use the grid to draw a few points using an x- and y- axis on graph paper it is much easier to immediately ‘see’ the whole line, calculate the slope, and find the x and y intercepts.

Drawing your own graph before using your graphic calculator engages the brain more and forms a stronger memory than only looking at a ready made textbook or calculator graph.

Translations, rotations, reflections and dilations are easily understood making a drawing on graph paper as well as vectors.

Dysgraphia

Just getting into the habit of using a separate square for each numeral or sign will land you those extra points you deserve in algebra, in particular when you also have dysgraphia.

Do not back off because using graph paper in class or for homework means you need to copy the question on your paper before starting to solve it. The copying (or errors in it) shows your teacher or parent that you have (or have not) read the question correctly.

In a nutshell

Graph paper can be used in multiple ways, such as for many arithmetic, measurement, algebraic, geometric, and recreational math purposes. It is also beneficial to students without Math problems and should be available in each math class, it should be dubbed ‘Math paper’.