Multplication-and-Division

Oct 1, 2026

The document outlines core multiplication and division teaching vocabulary and strategies, with an emphasis on building understanding from concrete models to pictorial and abstract methods. It covers repeated addition and equal groups, including times as big as, arrays, number line and partition approaches. It also describes a grid method recap, progressing to multiplying 3-digit numbers by 1 digit and column multiplication for larger numbers. Further sections address multiplying decimals up to two decimal places, aligning decimal points, using place value counters, and supporting reasoning with bar models and addition alleys.

LanguageEnglish

CategoryExam

FormatPDF

Pages17

Reading Time43 min

AccessFree to download

Multiplication and division key vocabulary

Concrete, pictorial, and abstract strategies

Grid method recap and progression

Column multiplication for multi-digit numbers

Bar modelling and number-line support

Multiplying decimals by a single digit

Place value and decimal alignment

| Key Vocabulary: groups of, lots of, times, array, altogether, multiply, count | | | | --- | --- | --- | | | | | | | | | | --- | --- | --- | | Key Vocabulary: groups of, lots of, times, array , altogether, multiply, count multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times. number line | | | | | --- | --- | --- | --- | | | | | | | Key Vocabulary: groups of, lots of, times, array, altogether, multiply, count multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times. number line | | | | --- | --- | --- | | | | | | Key Vocabulary: groups of, lots of, times, array, altogether, multiply, count multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times. number line partition, grid method, multiple, product, tens, units, value, inverse, multiple | | | --- | --- | | | | | Key Vocabulary: groups of, lots of, times, array, altogether, multiply, count multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times. number line partition, grid method, multiple, product, tens, units, value, inverse, multiple inverse | | | | | | --- | --- | --- | --- | --- | | Objective & strategy | Concrete | Pictorial | Abstract | | | Grid method recap from
year 3 for 2 digits x 1
digit
Move to multiplying 3 digit numbers by
1 digit. (year 4 expectation) | Use place value counters to show how we are finding groups of a number. We are multiplying
by 4 so we need 4 rows

Fill each row with 126

Add up each column, starting with the ones making any exchanges needed
| | | | | Column
Multiplication | |
|
Compact method
If children can not at first move to the compact method, they may need to use expanded first. See below.
| | | --- | --- | --- | --- | --- | | Key Vocabulary: groups of, lots of, times, array, altogether, multiply, count multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times. number line partition, grid method, multiple, product, tens, units, value, inverse, multiple square, factor, integer, decimal, short/long multiplication, ‘carry‘, quotient, prime number, prime factors, composite number (non-prime) | | | | | | | | --- | --- | --- | --- | --- | --- | --- | | Objective & strategy | Concrete | Pictorial | Abstract | | | | | Column Multiplication for 3 and 4 digits x 1 digit. | | | | | | | | Column
multiplication | Manipulatives may still be used with the corresponding long multiplication modelled alongside. |
Continue to use bar modelling to support problem solving | | Needing two addition alleys. The
first one, the numbers are crossed off 16 | | | | Key Vocabulary: groups of, lots of, times, array, altogether, multiply, count multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times. number line partition, grid method, multiple, product, tens, units, value, inverse, multiple tenths, hundredths, decimal, common factor, common multiple | | | | | | --- | --- | --- | --- | --- | | Objective & strategy | Concrete | Pictorial | Abstract | | | Multiplying decimals up to 2 decimal places by a single digit. | | | Remind children that the single digit belongs in the units column. Line up the decimal points in the question and the answer.
| | | Key Vocabulary: groups of, lots of, array, altogether, multiply, count, share, share equally, one each, two each…, group, groups of, lots of | | | | --- | --- | --- | | | | |

FAQs

What key models are used to teach multiplication progression?

The document uses concrete place value counters, pictorial approaches (such as arrays and bar modelling), and then transitions to abstract methods. It also recaps the grid method before moving to larger multiplications.

How does the grid method support multiplying 3-digit numbers by 1 digit?

It explains using place value counters to form equal groups and creating a grid with the appropriate number of rows (based on the multiplier). The method fills rows, then adds each column starting with the ones, making exchanges as needed.

What guidance is given for multiplying decimals by a single digit?

Children should remember the single digit belongs in the units column, and the decimal points in the question and answer must be lined up. The document targets decimals up to two decimal places.

Oct 1, 2026

Uploaded by Anna Hans