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HTU x TU Grid Multiplication Worksheets

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Grid multiplication.

Perform multi-digit multiplication operations using the grid method

This worksheet is a trainer for students not yet ready to take on multi-digit multiplication, or that need additional practice with the single-digit multiplication facts before moving on. Completing the grid helps reveal how the individual multiplication operations work to produce the result.

by Oxford Owl | Sep 12, 2016

How to: the grid method of multiplication

For some, maths homework is a breeze. For others, it’s a weekly chore. Just how do you engage children with something like multiplication? It’s (relatively) simple: encourage them to spot and understand the patterns. Here, former teacher and mathemagician Andrew Jeffrey shows us how to use the grid method of multiplication.

Written by Oxford Owl

Oxford Owl has been created by Oxford University Press to support children’s learning both at home and at school. Visit home.oxfordowl.co.uk for educational advice and activities.

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The Grid Method Framework

The grid method is a student-centered, competency-based framework , created at the classroom level and designed to fit any teacher’s style, within any curriculum, in any classroom. most importantly, it was built to reach all students…not just some..

Explore The Grid Method Mastery Framework in the  Teach Better Academy. 

The free academy course paints an overview of the framework, its design, and the effect on student growth and success., the full academy course workshop bundle provides educators an in-depth deep dive into the framework - walking you through the design and implementation process with a detailed workbook. conclude your course with a fully designed, student ready grid., the "building a grid live series" was originally aired as a live production in 2021 with grid method creator chad ostrowski. during each session, he was joined by a classroom educator from 1:1 coaching and feedback. you can access each discussion in a free course in the academy..

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The Grid Method for Long Division

• By Shelley Gray
• January 17, 2018

12 Comments

Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The  Grid method  is one of these strategies.

The Grid Method is intended for those who plan to teach traditional long division. It follows the same steps as traditional long division, but uses a different method of organization. This makes traditional long division easier for some students.

The Grid Method is not a mental math based approach. If you are looking for a mental math approach to long division, be sure to check out my posts for the  Box/Area Method  and  Partial Quotients. 

Let’s learn how to perform the Grid Method for long division!

Below, I have included both a video tutorial and step-by-step instructions.

VIDEO TUTORIAL:

STEP-BY-STEP INSTRUCTIONS

Suppose that we want to solve the equation 324÷2.

STEP 1: First we draw a grid. The number of sections in the grid depends on the number of digits in our dividend. For this equation, our grid will have 3 sections. We write the digits from 324 inside the grid, and we write our divisor (2) on the left side.

Now we ask ourselves, “How many times does 2 go into 12?” The answer is 6, so we write a 6 on top of the grid. Now we multiply 6×2 to make 12, and take that 12 away from 12. This leaves us with 0.

Now we ask ourselves, “How many times does 2 go into 4?” It goes 2 times, so we write a 2 on top of our grid. Now we multiply 2×2 to make 4, and take that 4 away from the 4. We are left with 0, which means that we have no remainder.

To find the final quotient, we simply list the digits from the top of the grid: 1, 6, 2. So 324÷2=162 .

LET’S TRY ANOTHER EXAMPLE

This time we will try an example that has a remainder. It also has more digits that our last example. Notice that when we have more digits in our dividend, we simply extend our grid. Let’s solve  6542÷5.

Here are the steps that we followed to solve this equation:

• Section 1: First we knew that 5 goes into 6 one time, so we wrote a 1 on top. We multiplied 1×5 to make 5, and took that 5 away from the 6, leaving us with a 1. We carried that 1 over to the tens place of the next section. Now we have 15 in that section.
• Section 2: We know that 5 goes into 15 three times, so we wrote a 3 on top. We multiplied 3×5 to make 15 and took that 15 away from the 15, leaving us with 0. We carried that 0 over to the tens place of the next section.
• Section 3: 5 does not go into 4, so we write a 0 on top, multiply 0x5 to make 0, and take that 0 away from the 4. This leaves us with 4. We carry that 4 over to the tens place of the next section, giving us 42 in the final section.
• Section 4: 5 goes into 42 eight times, so we write an 8 on top of the grid. We multiply 8×5 to give us 40, and take that 40 away from the 42, leaving us with 2. This means that our remainder is 2.
• To find our final quotient, we list the numbers from the top of the grid: 1, 3, 0, 8, and then add our remainder of 2.  So 6542÷5=1308 R2.

NEXT STEPS:

I would love to help you teach the grid method and other division concepts in your classroom. You may find the following resources helpful:

GRID METHOD TASK CARDS

These task cards give students the opportunity to practice the grid method for long division in a variety of different ways. Students will calculate quotients, solve division problems, figure out missing dividends and divisors, think about how to efficiently solve an equation using the grid method, and more. See the Grid Method Task Cards HERE or the Big Bundle of Long Division Task Cards HERE .

THE LONG DIVISION STATION

The Long Division Station is a self-paced, student-centered math station for long division. Students gradually learn a variety of strategies for long division, the grid method being one of them. One of the greatest advantages to this Math Station is that is allows you to target every student and their unique abilities so that everyone is appropriately challenged. See The Long Division Station HERE.

OR SEE ALL RESOURCES HERE.

I was wondering if there is a way to do problems such as 409 divided by 12? I’m looking for an easier method to do harder problems. Thank you!

I am concerned with teaching the grid method as a strategy for the division. Base ten place value and the ten to one relationship is an integral concept for whole number and decimal number computation. The grid method seems to be a trick or graphic organizer and does not bring out the place value or the relationship among the places, certainly, it does not conform with the “teaching for understanding” goal. Sadly, even though we encouraged preservice and in-service to carefully take advice or activities from the internet without investigating the research base they are busy and assume if it is on the web it must be OK. As a long time mathematics educator, I am concerned that the grid method is included in this posting.

Hi Vickie! Yes, you are correct in saying that this method does not use place value understanding. In the beginning of the blog post, that’s why I mentioned that this is NOT a mental math based approach, but can be used for those who are planning on teaching traditional long division (which also does not rely on place value understanding). I also address this in the video, but I’ll try to edit this post to make it more clear. I absolutely agree with you that teaching for understanding is vitally important. In this blog post I also link to posts on the partial quotients and box methods, which are much more mental math focused.

I like to show my students a variety of methods for dividing. Sometimes, you can teach them with conceptual understanding of place value time and time again, and they still don’t get it. I NEVER think teaching a different method, after you introduce using conceptual understanding, is a bad thing. You might actually have students who finally get it, and that is always a good thing.

I couldn’t disagree more. This method is 💯 rooted in place value. Each digit is in its own place value box. You could put all the zeroes in there (expanded form) for explaining purposes but then get them out to simplify the process. I substitute the numbers in the boxes with place value blocks on day 2 or 3 so they can see how this method is based on place value. It works well for showing why you regroup the leftover value as you move to the right. Don’t knock something until you try it and evaluate it thoroughly. This method is wonderful and there’s no reason to learn the standard way. This IS the standard way with a little extra organization.

You are correct in saying that this method doesn’t emphasize thinking about place value. However, does the standard algorithm really require thinking about place value? Most kids don’t even realize that they are working with place value. Asking “How many times does 12 go into 48?” pays no attention to whether that is 4800 or .048. It is only when students are asked to understand more deeply why the algorithm works that they focus on place value.

This method does not simplify using the long division algorithm and is less for working with multi-digit problems, so as Shelley says, it is a great intro to help kids break down the long division algorithm before learning it. I would add that this structure could also be used to teach polynomial division, as each term could go in its own distinct box.

I love this method. I think it will really help my scholars who are having trouble with long division. I have tried many methods and I am excited about trying this one! I also purchased your resource on TpT. Thanks again!

LOVE THIS!!! One of my students who struggles terribly with math was so excited to succeed with this today 🙂

One question: Does this method work with a divisor larger than one digit? The video only demo’d one-digit divisors.

I am trying to learn this method to better learn how to help my daughter who is learning this method in school. @J Riley i figured out a way to do this method with multi-digit divisors i will try to explain without the use of actual boxes. (lets assume each line is a new box each R will move into next box as normal) 12/6725=? 12 / 67 = 5 R7 12 / 72 = 6 R0 12 / 05 = 0 R5 (at this point we have a remainder of 5) so our answer is 560 R5 lets try a 3 digit divisor 120 / 64925 = ? 120 /649 = 5 R49 120 / 492 = 4 R12 120 / 125 = 1 R5 so our answer is 541 R5 as you can see from the examples for 2 digit divisors, divide first into the first 2 digits (if it will go , if not read further). For 3 digit divisors divide first into the first 3 digits ( if it will go , if not read further) now lets try an example where you can’t follow these steps 34 /12465 = ? 34 / 124 = 3 R22 34 / 226 = 6 R22 34 / 225 = 6 R21 so our answer is 366 R21 all you do is divide first into the first 3 digits remember each line is a different box in the box method so how i recommend teaching this with multi-digit divisors is instead of creating multiple boxes at the start create a new box each time you need one. Maybe Shelley Gray could create an example on the website that reflects this? but in the meantime just use the above examples try on a piece of paper recreating my examples in boxes ( remember each line is a new box). I know without a graphic “box” it maybe hard to visualize but try it out its the same principle just where you start whether you divide into the first digit or the first 2 digits etc. I hope this helps 🙂

I DO see place value in this method, as long as it is explained to the students. In the example above, the left-most box is the thousands place. After dividing the 6 thousands by 5, there is 1 thousand remaining. Regroup that thousand into hundreds. (There are 10 hundreds in 1 thousand. Add the 10 hundreds to the 5 hundreds already in the hundreds box.) And so forth.

It was very easy for me to explain this method to my son using place value, so that he understands why the process is working. Taking the first example 324 ÷ 2.

How many hundred times will 2 go into 300? We say how many hundred because this is the number we are going to write in the hundreds place. We can say how many times does 2 go into 3, and then multiply that by 100. It will go in 1 hundred times. We’ll write a 1 in the hundreds place.

100×2 is 200, so we’re going to subtract a 2 in the hundreds place. That’s the part we’ve already used. So now we have 1 hundred left. We’ll bring that 100 into the tens place. So now in the tens, we have 120 which we’re calling 12 tens. In the tens place, how many times can 2 go into 12 tens? 6 times. Since that’s in the tens place, it means 60, and 2 x 60 is 120.

And so on. My son’s really solid on place value and the meaning of each digit, so this explanation worked beautifully for him, and was much easier to visualize than if I’d used the same teaching style with the traditional method. It’s also more efficient to write, and leaves less room for copying or place value errors than partial quotient. It also lends itself much more easily to decimals than does partial quotient. All this is important because he is dysgraphic. The less he needs to write and line up, the better.

Very helpful! Thank you so much! My students will do really well with this. 🙂

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What is the grid method?

What is the grid method (or box method of multiplication)?

The grid method is a written method used to teach children multiplication. It involves partitioning numbers into tens and units before they are multiplied .

In some schools the grid method is referred to as the box method of multiplication because children learn to partition numbers into a grid of boxes.

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Multiplying a one-digit number by a two-digit number with the grid method

Multiplying a two-digit number by a two-digit number with the grid method

Children need to have the following skills before moving onto this next stage of the grid method:

• Good knowledge of times tables
• Able to multiply any number by 10
• Able to multiply a one-digit number by a multiple of ten (for example: 5 x 70, 2 x 30, 4 x 80 etc.)
• Able to multiply two multiples of ten (for example: 50 x 20, 80 x 30, 60 x 40 etc.) 
• A reliable written method for adding four numbers (some three-digit)

In Years 4 and 5 children move onto multiplying a two-digit number by another two-digit number.

Multiplying a three-digit number by a one-digit number with the grid method

In Years 4 and 5 , children are expected to be able to multiply a three-digit number by a one-digit number. This can also be done using the grid method:

Multiplying amounts of money with the grid method

It is very important when using the grid method to multiply amounts of money that children remember to keep writing £ or p next to the numbers so that they do not get confused about which unit of money they are dealing with.

Multiplying a decimal by a one-digit number with the grid method

Children in Year 6  are also expected to multiply decimals by one-digit numbers . Before moving onto this, children should be able to multiply decimals such as 0.5, 0.3, 0.8 etc. by a single-digit number mentally. This is a good way to teach this:

• First work out 4 x 7 = 28
• Then, because the 4 was actually 0.4, the answer needs to be divided by ten, so the answer is 2.8.

Multiplying a three- or four-digit number by a two-digit number with the grid method

However usually, at this stage, a child would use long multiplication (also called column multiplication) as a quicker method for these larger numbers.

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5 Reasons Why the Grid Method is Great for Teaching Drawing

What is the grid method and how can it help you teach your students to draw.

The grid method is a technique used in art that involves dividing an image into a series of smaller, more manageable sections using a grid. A grid is typically drawn over the reference image, and then students use the grid to draw the image on their own piece of paper, carefully replicating each section of the grid. This technique can be used to draw almost anything, including still lifes , landscapes , portraits , and more.

5 Benefits of Using Grid Drawings to Teach Drawing

Grid drawings can be a helpful tool for teaching drawing to your students for a variety of reasons. Here are some of the benefits:

• Grids can help students learn to draw accurately: By dividing the subject matter into smaller, more manageable sections, students can focus on drawing each part of the image accurately without becoming overwhelmed by the overall complexity of the subject.
• Grids can help students develop their observation skills: In order to draw each section of the grid accurately, students must pay close attention to the details of the subject matter and observe its features carefully.
• Grids can help students develop their spatial awareness: By drawing each section of the grid to scale, students can learn to think about the relationships between objects in the image and how they fit together in space.
• Grids can be used to introduce new techniques and skills: As students become more comfortable with using grids, they can be introduced to new techniques and skills, such as shading and perspective, to help them create more realistic and dynamic drawings.
• Grids can be used to draw a wide range of subjects: From still lifes to landscapes to portraits, grids can be used to draw almost any subject, making them a versatile and flexible tool for teaching drawing.

How to Help Students Who Struggle with the Grid Method

You’re always going to get some students who really struggle with grid drawings. This may be a reflection of some sort of spacial awareness problem or special need. One strategy that might help them is to create a viewfinder that is the exact size of the square, so they can isolate one square at a time. Using two L-shaped pieces of paper makes this easy. See the image below.

Artists Use Grids

Many artists use grids to scale up or transfer their drawings or photography onto canvas. Below is a Degas drawing that he made of his older sister. The grid was added so that he could scale up and transfer the drawing onto canvas. The resulting unfinished painting enlarges the composition by about fifty percent.

What are the Drawbacks of Using Grid Drawings?

There are a few potential drawbacks to using grid drawings as a teaching tool or as a drawing method. Here are a few potential negative sides to using grid drawings:

• Over-reliance on the grid: Some students may become overly reliant on the grid as a crutch and may struggle to draw accurately without it. It’s important to encourage students to develop their own observation and drawing skills, rather than relying solely on the grid.
• Limited creativity: Because grid drawings involve replicating an existing image, they may not allow for as much creative freedom as other drawing techniques. It is likely that you are going to want to include a range of drawing techniques in your curriculum. For example, direct observation and opportunities for students to create more gestural and experimental work.
• Time-consuming: Creating a grid and drawing an image using the grid can be a time-consuming process, especially for more complex subjects.

Overall, it’s important to consider the suitability of grid drawings for the specific subject matter and the goals of the drawing exercise and to balance the use of grid drawings with other drawing techniques and approaches.

Conclusion: To Grid or Not to Grid!

Grid drawings can be a helpful tool for teaching drawing and can be used to draw a wide range of subjects. They can help students learn to draw accurately, develop their observation skills and spatial awareness, and introduce new techniques and skills. However, it’s important to keep in mind that grid drawings may not be appropriate for every situation or subject matter.

When designing your lessons and curriculum, make sure you include a wide variety of drawing techniques and processes. This way, you will create a diverse, exciting and inclusive curriculum.

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The Arty Teacher

Sarah Crowther is The Arty Teacher. She is a high school art teacher in the North West of England. She strives to share her enthusiasm for art by providing art teachers around the globe with high-quality resources and by sharing her expertise through this blog.

2 responses to “5 Reasons Why the Grid Method is Great for Teaching Drawing”

Really helpful

That’s great to hear 🙂

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Using the grid method – the technique of applying a grid to a reference photograph in order to enlarge it on your work

The grid method has been used for centuries by artists as a tool to create correct proportions, from Egyptians carving figures to Leonardo da Vinci and many modern artists such as Jack Vettriano.

Drawing from a reference photo can be difficult. In order to ensure your proportions and composition are correct, the grid method can be used. 

To put it simply, the grid method breaks down your image into small, easy-to-draw segments of a larger image, ensuring they are copied correctly and are in the right proportions.

You can apply a grid to a reference image manually with a pencil and ruler, or digitally, using a PC or tablet.

To use the technique manually, get a hard copy of the image you want to use. You can work from a photograph, a page from a magazine, or a print-out of the image.

Once you have your reference image ready you can begin adding the grid (if working from a photo, you may wish to stick it onto a bigger sheet of paper to allow a margin).

Start by making evenly spaced marks around the outside of your image (or the section of the image you wish to draw). These will be the points from which the grid will form, so think about the size of each tile you want to end up with (we have gone with 2cm). Continue the marks around all four sides.

Note: Consider the size and format of your finished image as, for example, you may wish to translate a landscape image into a portrait format.

The next step is simple – joining the horizontal and vertical marks to form the grid. Once the grid is in place, label each axis, the horizontal with letters and the vertical with numbers, for example. This will make it easier to find specific squares when drawing from the grid.

If you are creating the grid using a PC or tablet (which many artists do now), find the image you wish to copy or take a photo using the device. You can open the image in an editing program and apply a grid over the top (many programs offer a grid but if not you could draw out a grid using a line tool). Keeping the image on a screen with a grid drawn on top allows you to zoom in and move the image around with the grid staying in place. This is useful for focusing on individual squares of the grid if you are looking for small details.

Whether you have drawn the grid by hand, or you have superimposed one onto your image digitally, the technique is the same from now on.

Now the image you wish to copy is gridded up, we need to focus on the artwork you are going to make.

Start by getting the canvas, paper, or whatever ground you wish to work on (for our version we have used a canvas). Draw a new grid onto the canvas in pencil (lightly if possible). Make the grid the same shape as the one on your photo. For example, if your original grid is 14 squares x 9 squares like ours, make the new grid the same.

If you wish to enlarge or decrease the proportions of the original, simply carry out the following calculations (using a calculator if necessary):

1. Measure the width of your canvas, board or paper.

2. Divide that figure by the number of squares on the width of your gridded image (e.g., our canvas is 100cm wide and our gridded photo is 14 squares wide, so 100÷14 = 7.1cm)

3. Mark out points across all four sides of your canvas separated by the answer to your sum (7.1cm apart in our example).

4. Join the points to create a grid and you will have a perfectly scaled-up version of your reference grid. Mark the axes with numbers and letters, the same as you did with your reference grid.

Your grid is now ready to use.

The hard work is over – all that is left to do is use the grid for your drawing. All you have to draw is the detail from each square, breaking the image down into a series of tiny ones rather than the whole. You can start anywhere on the grid you like – if you lose the tile you are working on, simply use the axis letter and number to find it, e.g. tile G5 on the image below.

Continue working tile by tile until your drawing is complete.

Once you are happy with the sketch you have created using the grid, you can remove the gridlines lines with an eraser. Continue to work on the image, whether it be in paint, pencil or any other medium.

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Grid Method

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

22 February 2018

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Worksheet for using the grid method for multiplication.

Other topics covered: Numbers

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