Understand
Why ×11 works
Use 11 = 10 + 1 and the distributive property: 11n = 10n + n.
Mathematics · Grade 5
Build multiplication, fraction and decimal reasoning.
Grade 5 now connects efficient multiplication strategies with fraction area models and decimal place value. Learners understand why shortcuts work before using them.
Available now
Multiply by 11 Lab
Understand 11 × n as 10n + n, then practise the two-digit mental shortcut with and without carrying and generalise the same distributive idea to 12, 21 and 101.
Practise
Use the shortcut
For two-digit numbers, combine the outside digits with their sum in the middle and handle carrying correctly.
Generalise
Split other multipliers
Extend the same place-value thinking to 12n, 21n and 101n.
Available now
Fraction Multiplication Area Lab
Multiply proper fractions by building an area model: rows show one factor, columns show the other, and the overlap shows the product.
Understand
See the overlap
Partition one whole in two directions and connect the overlapping cells to the product fraction.
Practise
Multiply across
Connect the model to numerator × numerator and denominator × denominator.
Review
Simplify
Recognise equivalent products and reduce fractions when a common factor remains.
Available now
Decimal Place Value Lab
Work with numbers through thousandths and connect four representations of the same decimal.
Place value
Locate each digit
Identify ones, tenths, hundredths and thousandths and understand the value of a highlighted digit.
Representations
Standard ↔ expanded
Move between a decimal and the sum of the place-value parts that compose it.
Language
Read decimals in words
Connect decimal notation with precise word form, including values such as forty-two thousandths.
Also available
Mental Math Shift Lab
Build decimal fluency by adding and subtracting 0.1 and 1 mentally.
Also available
Place Value & Expanded Form Lab
Practise decimal decomposition through thousandths using fresh generated challenges.