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Content Area: Math
Index: 4.3A Grade 4 CPI 1
Standard: 4.3 - Patterns and Algebra
Strand: A - Patterns
Cumulative Progress Indicator: 1 - The student will recognize, describe, extend, and create patterns · Descriptions using words, number sentences/expressions, graphs, tables, variables (e.g., shape, blank, or letter) · Sequences that stop or that continue infinitely · Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11, . . . or 800, 400, 200, . . .) · Sequences can often be extended in more than one way (e.g., the next term after 1, 2, 4, . . . could be 8, or 7, or … )
Grade: 4
Sample Activities:
· Students make a pattern book that shows examples of patterns in the world around them.
· Students use pattern blocks, attribute blocks, cubes, links, buttons, beans, toothpicks, counters, crayons, magic markers, leaves, and other objects to create and extend patterns. They might describe a pattern involving the number of holes in buttons, the number of sides in a geometric figure, the shape or the thickness of objects.
· Students use sequences of letters or numbers to identify the patterns they have created.
· Students investigate the sum of the dots on opposite faces of an ordinary die and find they always add up to 7.
· Students solve two-dimensional attribute block patterns where, for instance, each column is a different shape and each row is a different color. They should be able to choose the block that fills in the missing cell in such patterns.
· Students count by 2, 3, 4, 5, 6, 10 and 12 on a number line, on a number grid, and on a circle design.
· Students begin with numbers between 50 and 100 and count backwards by 2, 3, 5, or 10.
· Students create patterns with the calculator: They enter any number such as 50, and then repeatedly add or subtract 1 or 2 or 3 etc. If, for example, they enter 50+1=== ... , the calculator will automatically repeat the function and display 51, 52, 53, 54, ... . Some calculators may need to have the pattern entered twice: 50+1=+1=== ... . Others may need 1++ 50=== ... .
· Students begin with a number less than 10, double it, and repeat the doubling at least five times. They record the results of each doubling in a table and summarize their observations in a sentence.
· Students read Anno's Magic Seeds by Mitsumasa Anno. In it, a wizard gives Jack two seeds and tells him that if he eats one, he won't be hungry for a year and if he plants the other one, two new seeds will be formed. Jack continues in this way for awhile and then tries other schemes that produce even more new seeds. The students work in groups to make charts and tables to show how many seeds Jack has at given points in time. As an individual assessment assignment, students are asked to find how many seeds Jack has after ten years using one of the discovered patterns and to support their answers in writing and with tables.
· Students supply the missing numbers on a picture of a ruler which has some blanks. Then they explore how to find the missing numbers between any two given numbers on a number line. They extend this to larger numbers; they might label each of five intervals from 200 to 300 or each of four intervals from 1,000 to 2,000.
· Students investigate number patterns using their calculators. For example, they might begin at 30, repeatedly add 6, and record the first 10 answers, making a prediction about what the calculator will show before they hit the equals key. Or they might begin at 90 and repeatedly subtract 9.
· Students do comparison shopping based on items that are for sale in multiples. For instance: If chewing gum is sold at 3 packs for 85 cents (p = 85/3), is that a better or a worse buy than a single pack for 30 cents (p = 30)? They sort their examples into groups where the multiple buy is a better deal, the same deal, or a worse deal than the single package deal.
· One student has been folding origami cranes to send to Hiroshima for Peace Day in August. He brings the 47 cranes that he has folded so far to class and asks for help to fold many more. The class decides to have each of the 26 students fold one crane each week for the rest of the school year. The teacher asks groups of students to find a way to determine how many cranes will be in the collection after some given number of weeks. They figure out whether they can reach 500 cranes by the end of the year.
· Using the constant multiplier feature of a calculator, students see how many times 1 must be doubled before one million is reached. They might first guess the number of steps to one million, and to half a million.
· Students start with a long piece of string. They fold it in half and cut it in two, setting aside one piece. Then they take the remaining half, fold it in half, cut it apart, and set aside half. They continue this process. They discuss how the length of the string keeps getting smaller, half as much each time, so that after about ten cuts, there is essentially no string left. Some students may understand that the process could keep going for several more steps, if we could only cut more carefully, and some may realize that in theory the process could continue forever.
· Students count out 1, 2, 3, 4, 5, 6, ... , and recognize that this pattern could continue forever. They also count out other patterns, like the even numbers, or the square numbers, or skip-counting by 3s starting with 2, and recognize that these patterns also could be continued indefinitely.
· Students investigate the growth patterns of sunflowers, pinecones, pineapples, or snails to study the natural occurrence of spirals.
Sample Assessment Questions:
· Open Ended Question: Patterns and Algebra
· If this pattern continues, what is the next number? 5, 8, 7, 10, 9, 12, 11 o A. 14 o B. 13 o C. 12 o D. 10
The correct answer is A.
Kidspiration Activities:
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