Bar Models and Unknown Equations
Year 4 Mathematics Exploring multiplication and division through visual models Finding unknown quantities
What Are Bar Models?
Visual tools that help us see mathematical relationships Show equal groups and totals Help us write equations with unknowns Make abstract math concepts concrete
Let's Explore Our First Bar Model
Look at the three bars with 15 on each Find the bar with the question mark (?) How can we arrange them to show they're equal? What do you notice about the lengths?
From Bar Models to Equations
3 groups of 15 equals the unknown We can write this as: 3 × 15 = ? The multiplication shows 3 equal groups Each group contains 15
Can You Think of Other Equations?
We wrote 3 × 15 = ? What other equations can we make? Think about division... How could we split the unknown into equal parts?
Division Equations from the Same Model
? ÷ 3 = 15 (total divided by number of groups) ? ÷ 15 = 3 (total divided by amount in each group) Same bar model, different equations! All equations are connected
New Challenge: Two Different Bar Types
2 bars showing 12 each 3 unknown bars of equal size Arrange them to show equivalence What equations can you see?
More Complex Equations
2 × 12 = 3 × ? (two multiplications equal each other) We can also write: 2 × 12 ÷ 3 = ? Or: 3 × ? ÷ 2 = 12 Multiple ways to show the same relationship
Finding Unknown Groups
Total bar shows 21 Each small part shows 3 How many groups of 3 make 21? The number of groups is unknown
What We've Learned Today
Bar models help us visualize mathematical relationships One model can show multiple equations Multiplication and division are connected Unknowns can represent totals, group sizes, or number of groups Visual models make abstract math concrete