Multiplication using mental math

Have you ever tried to fit pieces of furniture into a space, tried to separate items into equal groups, calculate the area of a rectangular room, or set up a tray of muffins on a platter? You may not have realized that you were actually doing multiplication. Multiplication is when we use repeated addition, arrays, or multiple equal groups to calculate the total. Multiplication comes in many shapes and forms and we use it on a regular basis with our day-to-day activities. If a baker was to make 4 trays of 12 cookies, how many cookies would they have in total? To answer this question, you would need to figure out 12 × 4. What strategies or steps would you take to complete this? What tips about multiplication could help you figure it out?

Multiplication strategies

Let’s review some strategies that we can use to help us multiply large numbers.

Matrix method

Let’s explore the following video entitled “Matrix Multiplication” to learn how to use a matrix to multiply 2-digit by 1-digit numbers using mental math.

Expanded form

Factor trees

Factor trees are also helpful when you are separating numbers into their place value because even though it could be easy to multiply 40 and 2 with 30 and 5 as demonstrated in this example, sometimes other numbers need to be divided up further to multiply quicker. For example, 94 might be okay to represent as 90 and 4 but it can also be expanded into 3 × 30 and 4.

Let’s examine the following image with a diagram of a factor tree for the number 60:

Algorithm

Multiplying decimals

Don’t forget that when you multiply using decimals, you can first ignore the decimals and multiply. Then, count how many decimal places are being used in the two numbers. In the following example, there are three decimal places in total. You would then add the decimal to your number, starting at the right of your number and counting three decimal places over.

Task: Maximizing area

The city has decided that they will be building a new rectangular-shaped community centre. It has found a vacant piece of land that is 45.3 m wide maximum. They could purchase less if they prefer. They haven’t decided on the depth of the building yet. However, they know that the total area cannot exceed 2,000 square meters. Area is the length × width. For example, we could suggest that the dimensions are 5 m × 10 m but that wouldn’t be large enough or really take up the allotted space. What are some possible dimensions of this new community centre? What would be the best use of space and create the maximum area?

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the fillable worksheet.

Everyday expenses

Imagine that the bus in a city or town costs $2.25 for a one ride fare, $10.75 for a weekly pass, and $45 for a monthly pass. How many days would a rider need to ride the bus before it becomes a better deal to purchase the monthly pass? Use two different multiplication strategies to find your answer. If possible, compare your answers with a partner. Which strategy did you find easiest to use?

If you would like, you can complete this activity using TVO Mathify.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Connect with a TVO Mathify tutor