Chapter 6 · Consolidation and enhancement
Lesson 6.10 · Mathematics plaza — repeated pattern problems
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Identify the repeating unit in a shape or number pattern.
- 02Find the $n$th term (e.g. 102nd).
- 03Sum the first several terms when useful.
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.OA.D.9 | Identify arithmetic patterns. |
| 3.OA.A.3 | Multiply/divide to solve word problems. |
| 3.OA.D.8 | Two-step word problems. |
| 3.OA.C.7 | Fluently multiply and divide within 100. |
| 3.NBT.A.2 | Add/subtract within 1000. |
| 3.NBT.A.3 | Multiply one-digit × multiples of 10. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Patterns | Repeating cycles | G3 OA |
Core Concepts
Repeated patterns — shapes and numbers.
Find the Cycle
Shape sequence: find the repeating block length.
Nth Term
Numbers $1,3,2,4,\ldots$ — what is the 102nd?
Sum of First Terms
Find the sum of the first several numbers in the pattern when asked.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Repeated pattern | A sequence that cycles through the same unit. |
| Nth term | The item in position n. |
Key Answers
Quick reference for this lesson’s exercise answers.
Key answers
- Shape sequence: (1) $107$th is $\triangle$;\; (2) $47$ triangles
- Calendar: (1) $52$ weeks $1$ day;\; (2) max $5$ Sundays in December;\; (3) Monday
- Multiple choice: (1) A ($21$ yellow);\; (2) B (red)
- Cards: (1) D gets the $28$th;\; (2) with $54$ cards, last to B ($14$ cards)
- Number cycle: (1) $3$;\; (2) sum $254$
- Children’s Day: $2012$ Friday; $2013$ Saturday
- Enhancement: (7) column $47$ → A3;\; (8) $1$ Oct was Thursday;\; (9) $25$ illustration pages