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Level Four > Number and Algebra

# Cross Products

Keywords:
Purpose:

These exercises and activities are for students to use independently of the teacher to practice number properties.

Specific Learning Outcomes:
solve decimal multiplication problems using place value
solve 2 digit by 2 digit multiplication problems using place value
solve decimal by 2 digit whole number multiplication problems using place value
solve decimal by decimal multiplication problems using place value
Description of mathematics:
Multiplication and division,  AM  (Stage 7)
Multiplication and division,  AP  (Stage 8)
Required Resource Materials:
Practice exercises with answers (PDF or Word)
Activity:

### Prior knowledge

recall multiplication facts
multiply by multiples of 10
understand the area model of multiplication
solve 2 digit by 2 digit multiplication problems using place value

### Background

This activity uses place value partitioning to solve multiplication problems. It uses the area model. This activity involves whole numbers and decimals in the problems. While the drawings involve using an area model to display the multiplications, (so the size of each box is in some form of proportion to the size of the numbers), it should also be noted that students can do the same problems using a table (or tabular form). In this form area is not considered.

For example: 14 x 51 can be done by using the following table (where all the boxes are the same size).

Exercise 1
Asks students to solve 2 digit by 1 digit multiplication using the area model to show place value multiplication. It is designed to follow on from a teaching episode in which the strategy is illustrated and used by the students. Once students have convinced themselves that the strategy works with a range of simple numbers they are ready to explore more difficult numbers including decimals.

Exercise 2
Asks students to fill in unknowns in 2 digit and 1 digit multiplication. Being able to multiply by multiples of 10 is central.

Exercise 3
Asks students to use the same strategy as in exercise 2 to work backwards but introduces diagrams oriented vertically. This exercise would work well as a homework exercise. I

Exercise 4
Asks students to solve multiplication problems where a decimal number (1 dp) for one of the factors.

Exercise 5
Asks students to solve multiplication problems with whole numbers between 10 and 100 for both factors.

Exercise 6
Asks students to solve multiplication problems where one of the factors is a one place decimal and the other factor is a whole number between 10 and 100.

Exercise 7
Asks students to solve multiplication problems where both factors are one decimal place decimals, using numbers less than 10 until the last question which is greater than 10.

Exercise 8
Asks students to find unknowns in problems that involve two decimals to 1dp.

Exercise 9
Asks students to solve word problems. Students may need to be encouraged to use units appropriately.

Exercise 10
Asks students to investigate the use of the strategy for numbers in the 100s

Exercise 11
This exercise introduces x as a length added to both sides of the rectangle and requires students to multiply the algebra and add like terms.

AttachmentSize
CrossProductsSheet.pdf184.06 KB
CrossProductsSheet.doc398 KB

## Writing in Words and Symbols

These exercises and activities are for students to use independently of the teacher to develop and practice algebraic reasoning. They follow from teaching sessions that are described below. The initial teaching episode is an attached lesson, while other teaching sessions are outlined in the ‘background’ section.

## Multiplication Strategies

These exercises and activities are for students to use independently of the teacher to practice number properties.

## The difference of two squares

These exercises and activities are for students to use independently of the teacher to practice number properties

## Divide and Conquer

This is a collection of activities to enhance and extend division skills and understanding.

## Homework sheet: stage 6 – 7, Revision of add-sub and mult-div 2

These exercises and activities are for students to use as a week’s homework to practice number properties