Mathematics Grade 1: Patterns and Sequences

Grade 1 Mathematics: Patterns and Sequences

1. The Driving Question

"If you’re lining up your crayons—red, blue, red, blue—and your friend adds a green one, why does it feel ‘wrong’? How do you know what comes next in a row of shapes, sounds, or even dance steps?"

2. The Core Idea — Built, Not Listed

Imagine you’re making a bead bracelet for your best friend. You start with a red bead, then a yellow, then red, then yellow. Your friend says, "I want the next one to be blue!" But something feels off—like when you clap twice, stomp once, clap twice, stomp once, and then someone stomps twice instead of clapping. The bracelet (or the clapping game) has a pattern: a rule that tells you what comes next, over and over.

Patterns aren’t just about colors or sounds—they’re about predictability. If you know the rule, you can guess what’s coming, like how every other step in a hopscotch grid is a square you jump on with both feet. The rule could be "add one more" (like 2, 3, 4, 5) or "switch back and forth" (like circle, square, circle, square). Once you spot the rule, the pattern isn’t magic—it’s math you can see and do.

Key Vocabulary: - Pattern: A rule that repeats in the same order. Example: The "ding-dong" sound your doorbell makes is a pattern—it never goes "dong-ding" unless someone’s messing with you. - Sequence: A list of things (numbers, shapes, sounds) that follow a pattern. Example: The sequence of days in a week (Monday, Tuesday, Wednesday...) repeats every 7 days. - Core: The smallest part of a pattern that repeats. Example: In the pattern clap, snap, clap, snap, the core is clap, snap—just those two moves. - Extend: To add the next part of a pattern using the rule. Example: If the pattern is ?, ?, ?, ?, extending it means adding ? next.

3. Assessment Translation

How this appears in class: - Exit tickets: "Draw the next two shapes in this pattern: ?, ?, ?, ?, _, _." - Show-your-work problems: "Color the next three beads in this bracelet: red, blue, red, blue, _, _, ____." - Oral explanations: "Tell your partner the rule for this pattern: 5, 10, 15, 20."

What "proficient" looks like vs. "developing": | Proficient | Developing | |----------------|----------------| | Draws the next two shapes correctly (?, ?, ?, ?, ?, ?). | Draws one shape correctly but the second is wrong (?, ?, ?, ?, ?, ?). | | Explains the rule in words ("It goes red, blue, red, blue"). | Points to the pattern but can’t describe the rule. | | Fixes a broken pattern ("This should be 2, 4, 6, 8, not 2, 4, 7, 8"). | Doesn’t notice the mistake. |

Model student response (proficient): Prompt: "What comes next in this pattern? ?, ?, ?, ?, _, _" Response: "The next two are ?,-because the pattern is apple, banana, apple, banana. It keeps switching."

4. Mistake Taxonomy

Mistake 1: Skipping the core - Prompt: "Draw the next two shapes: ?, ?, ?, ?, ?, ?, _, _" - Common wrong response: ?, ? (student repeats the first shape instead of the core). - Why it loses credit: The student sees the first shape and assumes it’s the rule, not the whole repeating part (?, ?, ?). - Correct approach: Circle the core (?, ?, ?) and say, "The core repeats, so next is ?, then ?."

Mistake 2: Counting instead of repeating - Prompt: "What comes next? 3, 6, 9, 12, ____" - Common wrong response: 13 (student adds 1 instead of 3). - Why it loses credit: The student counts up by 1s (a simpler rule) instead of spotting the +3 pattern. - Correct approach: Say, "3 + 3 = 6, 6 + 3 = 9, so 12 + 3 = 15."

Mistake 3: Ignoring the format - Prompt: "Color the next bead: red, yellow, red, yellow, ____" - Common wrong response: Leaves it blank or colors it purple (student doesn’t use the given colors). - Why it loses credit: The pattern’s rule is about which colors, not just "any color." - Correct approach: Say, "It’s red, yellow, red, yellow, so next is red."

5. Connection Layer

• Within math: Patterns-Skip counting — If you can extend a pattern like 5, 10, 15, 20, you’re already doing skip counting by 5s.
• Across subjects: Patterns-Music — The "verse-chorus-verse" structure in songs is a pattern, just like shapes or numbers.
• Outside school: Patterns-Traffic lights — Red, yellow, green, red, yellow, green isn’t random; it’s a pattern that keeps drivers safe.

6. The Stretch Question

"If a pattern starts with 1, 2, 4, 8, what’s the rule? What would the next three numbers be? Could this pattern ever include the number 5?"

Pointer toward the answer: The rule isn’t "add 1" or "add 2"—it’s "double the last number" (1×2=2, 2×2=4, 4×2=8). The next three numbers would be 16, 32, 64. The number 5 can’t be in this pattern because you can’t double a whole number to get 5 (2.5×2=5, but we’re only using whole numbers here). This is how some patterns grow instead of just repeating!