1 Counting Embedded Figures Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: With this lesson, students can recognize a connection between algebraic and geometric concepts. They gather data about embedded figures, look for patterns within the data, engage in mathematical discussions, construct their own ideas, and form generalizations.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 5–7 Professional Commentary: In this lesson, students explore the Fibonacci series. They identify the pattern among the Fibonacci numbers, look for applications of these numbers, and explore the ways that this pattern can be related to objects and shapes in both the natural and designed world.... Resource Type: Lessons Discipline: Mathematics Grades: Grade 6 Professional Commentary: This two-lesson unit allows students to investigate the triangular numbers in an interesting, real-world context, the Supreme Court. Beginning with the classic handshake problem, students generate geometric and algebraic representations for the patterns they encounter and conclude with a formula for the nth triangular number.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 7–8 Professional Commentary: Students explore the Fibonacci sequence using a table, spreadsheet, and scatterplot. Students build a spreadsheet and use it to determine that the ratio of two consecutive Fibonacci numbers approaches the Golden Ratio. Lesson resources, including suggested web sites, highlight many real-life examples of the Golden Ratio.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 5–8 Professional Commentary: This lesson emphasizes discerning patterns and developing general rules for the nth term of a sequence. Using an eighth grade TIMSS item (how many small triangles are subsumed in a sequence of increasingly large similar triangles), students look for patterns, find a general rule, and express the rule using a variable.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 4–5 Professional Commentary: Students explore and find rules for a growth pattern in snakes. The teacher presents students with rules for a growth pattern that involves red and black rings in imaginary snakes.... 7 Rectangle Pattern Challenges Resource Type: Lessons Discipline: Mathematics Grades: Grades 5–9 Professional Commentary: Students analyze three stages of a colorful rectangular pattern, and then determine the composition of future stages. Younger students can describe in words how the pattern grows, while older students can find algebraic expressions for the number of blocks of each color in the pattern.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 3–5 Professional Commentary: Students must use numerical and geometric logic to crack the double pattern that unlocks the Poddles' cyberpower vault before Hacker and his henchmen do! In this lesson, students visit the Cyberchase Club website to learn that patterns can repeat or change in more than one way at a time.... 9 The Yo-Yo Problem: Solving Linear Equations Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–10 Professional Commentary: Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation, and the graphing calculator. The lesson starts with the presentation of the yo-yo problem.... 10 NAEP Assessment Item, Grade 8: Find Number of Diagonals in a Polygon from a Vertex Resource Type: Assessments Discipline: Mathematics Grades: Grades 5–7 Professional Commentary: Given the number of diagonals that can be drawn from a vertex in a 4-, 5-, 6-, then 7-sided polygon, students must determine how many diagonals can be drawn from a vertex in a 20-sided polygon. This constructed-response question is a sample test item used in grade 8 in the 1996 National Assessment of Educational Progress... |