Cogito
Grade 3 Math · Chapter 7 · Lesson 4
Patterns and Explaining Them
Spotting a pattern is half. Saying why is the other half.
10 problems · about 13 minutes · 3.OA.D.9
What this lesson teaches
The child identifies arithmetic patterns and explains them using properties of operations.
- Every pattern in the tables has a reason.
- Knowing the reason lets you predict safely.
- A pattern without a reason might fail on the next case.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Two-Step Problems With All Four Operations: 9 × 6 − 20 = ?
Answer 34
Why 9 × 6 = 54, and 54 − 20 = 34.
Review — Equal Areas of a Shape: A shape split into 7 equal parts. What is the denominator of one part?
Answer 7
Why Each part is 1/7 of the shape.
Review — The Quadrilateral Family: How many sides does every quadrilateral have?
Answer 4
Why All quadrilaterals have 4 sides.
Warm Up
Straightforward practice. Get the method working first.
3 problemsThe 9 times table goes 9, 18, 27. What comes next?
Answer 36
Why 27 + 9 = 36.
Why is spotting a pattern not enough?
Answer Without a reason it might fail later.
Why The reason is what makes a pattern safe to rely on.
The 8 times table goes 8, 16, 24. What comes next?
Answer 32
Why Add 8.
Build It Up
The same ideas with more to keep track of.
1 problemIs 6 + 8 odd or even?
Answer Even
Why Both are even.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsIs 5 + 8 odd or even?
Answer Odd
Why One odd and one even leaves one over.
The Next One: The 7 times table goes 7, 14, 21, 28. What comes next?
Answer 35
Why 28 + 7 = 35.
Odd and Odd: Is 7 + 9 odd or even?
Answer Even
Why Odd plus odd is always even.