Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A pattern rule such as "start at 1 and add 3" tells you exactly how to build a sequence: 1, 4, 7, 10, 13 and so on. Fourth graders generate terms like these, but the real work is noticing what the rule never mentioned. In that sequence the terms alternate odd, even, odd, even. The rule says nothing about odd and even, yet the pattern shows it, and students are asked to explain informally why it keeps happening: adding an odd number to an odd number gives an even number, and adding it to an even number gives an odd one.
Shape patterns work the same way. A rule like "triangle, square, square, repeat" lets students predict the 20th shape without drawing all twenty, because the pattern cycles every three shapes. Spotting hidden features, testing them on more terms and giving a reason is early algebraic thinking that leads directly to the numerical patterns and ordered pairs of fifth grade.
With "add 4, start at 2," some students compute the 5th term as 5 + 4. Remind them the rule acts on the previous term, so build the list: 2, 6, 10, 14, 18.
Students may claim every term ends in 5 after seeing two terms. Encourage them to generate several more terms before stating a feature.
"It goes odd, even, odd" is an observation, not a reason. Prompt with "What happens when you add 3 to an odd number?" to move toward an explanation.
Start at 5 and use the rule "add 10." Write the first five terms and describe a feature the rule does not mention.
Answer: The terms are 5, 15, 25, 35, 45. Every term ends in 5, because adding 10 never changes the ones digit.
Let students invent rules for a partner and then trade lists to hunt for hidden features. Rules that add an even number, an odd number or a multiple of 10 produce very different features, which makes for rich comparison.
For shape patterns, ask students to label the repeating unit and count its length. Tests often ask for the shape in a far position such as the 25th, and dividing by the unit length (using the remainder) solves it without drawing.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 23
The terms are 3, 7, 11, 15, 19, 23. The rule is applied 5 times to reach the 6th term: 3 + 5 × 4 = 23.
Answer: B) The terms alternate between odd and even
The rule states "add 3" and "start at 1". The odd, even, odd, even pattern is a feature you notice. The terms are not multiples of 3 (1, 4, 7 are not).
Answer: A) circle
The unit has 3 shapes. Positions 1, 4, 7 and 10 are all circles, because 10 ÷ 3 leaves a remainder of 1.
Answer: 32
The terms are 50, 44, 38, 32. Three subtractions of 6 bring 50 down to 32.
Answer: C) Because adding an even number to an even number always gives an even number
The first term, 2, is even, and even + even is always even. So every term stays even.
Answer: 34
Each term is 9 more than the one before: 25 + 9 = 34, and 34 + 9 = 43 checks.
A full lesson with slides, activities and an exit ticket on number and shape patterns, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.OA.C.5 with an answer key, ready in about a minute.
Make a worksheet →Turn number and shape patterns into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A rule tells you how to get from one term to the next, such as "add 5" or "multiply by 2," together with a starting term.
No. They describe and explain patterns in words. Using expressions and ordered pairs for patterns starts in fifth grade with 5.OA.B.3 and grows in middle school.