Max Product

Introduction

In mathematics, a product is the result of multiplication.

For the following task, you will be finding different products WITHOUT a calculator.  You may wish to remind yourself how to multiply by watching the following videos: grid method, column method or lattice method.

If we choose the numbers 2, 5, 6, 8 to begin with, how many different products with two 2-digit numbers can we make?  One of them is 25 x 68.  List them all, be systematic with your approach!

Now do the multiplications.  Which one gives you the biggest value (max product)? Which one gives you the smallest value (min product)?

Now choose four DIFFERENT NON-ZERO digits

List all the different products with two 2-digit numbers and do the multiplications.

Which gives you the max product?  Which gives you the min product?

Repeat this a few times,  can you come up with a rule of how we can always get the max product?  What about the min product? (You may wish to use the picture on the below to help you)

Further Questions and Challenges

In the previous part, you had different products with TWO 2-DIGIT numbers?  What if they DON'T have to be 2 DIGIT numbers?  For example, if we choose the numbers 2, 5, 6, 8, then one multiplication could be 2 x 568.  How many different multiplications can you then have?  List them all, be systematic with your approach!

Do the multiplications.  Which gives you the max product?  Which gives you the min product?

Can you come up with a rule of how we can always get the max product?  What about the min product?

Now choose FIVE DIFFERENT NON-ZERO digits

List all the different products with a 3-digit number multiplied by a 2-digit number. For example,  if we choose the numbers 2, 5, 6, 8, 9, then one multiplication could be 256 x 89.

Do the multiplications.

Which gives you the max product?  Which gives you the min product?

Which combination gets you the closest to 50,000?

Repeat this a few times,  can you come up with a rule of how we can always get the max product?  What about the min product?

Further Practice 

An essential skills introduced in this lesson is multiplication.  You may also wish to practise division as well as the four operations with negative numbers.  Do the relevant skills practice on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.  Watch any video and/or go through any online lesson as you see fit.

Transum

• Times Square - practise your times tables with this self-checking multiplication grid.

• Pairs 240 - find the pairs of numbers that multiply together to give a product of 240 in this collection of matching games.

• Three Ways - find three different ways of multiplying four different digits together to get the given target number. There are nine levels for this online challenge.

• Formal Written Methods - examples of formal written methods for addition, subtraction, multiplication and division.

• Number Skills Inventory - a checklist of basic numeracy techniques that every pupil should know.  Look especially at the adding and subtracting activities.

• Mix and Math - determine the nature of adding, subtracting and multiplying numbers with specific properties - not everything here is relevant.

• What Are They? - an online exercise about sums, products, differences, ratios, square and prime numbers - not everything here is relevant.

Negative numbers

• Boxed In Numbers - the classic dots and boxes game with the addition of some positive and negative numbers which determine your score.

• Negative Magic - four partially completed magic squares containing negative numbers. Fill in the missing numbers.

• Negative Numbers - use negative numbers in basic arithmetic and algebraic calculations and word problems.

• Reading Scales - a self marking exercise on the reading of scales of different types.

• Temperatures - test your understanding of negative numbers with this self marking quiz about temperatures.