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Geometry Across the Grades & Standards. Presented by Keith Smith Pacent Learning Solutions, Inc. Agenda. Introduction Background of Presentation Cross Curricular Matrix: Area and Perimeter Grade 3 Sample Lessons Grade 4 Sample Lessons Grade 5 Sample Lessons
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Geometry Across the Grades & Standards Presented by Keith Smith Pacent Learning Solutions, Inc.
Agenda • Introduction • Background of Presentation • Cross Curricular Matrix: Area and Perimeter • Grade 3 Sample Lessons • Grade 4 Sample Lessons • Grade 5 Sample Lessons • Activity: Cross Curricular Matrix: Angles • Wrap-Up
Background Two teachers with the same problem 3rd Grade & Algebra Readiness A = L ● W P = 2L ● 2W UNITS? Inches or square inches
Background • Time and Creativity No Time to Re-teach! No Time for favorite activities!
Background • Teaching choices are often 25% - 40% off standard • Often add levels of difficulty that go beyond standard. • Whole lessons and/or concepts are not grade level.** ** This does not mean kids can’t do the math or that it’s not grade level appropriate. It just might not be a priority. Instead of extending “concept development” we extend “difficulty”. (Ex. Equivalent Fractions) Instead of backward planning from a good assessment we cover the lessons.
Background • Goals • Prioritize instruction (Focus on what’s most important). • Work to extend concept development on priorities. • Look for opportunities to pre-teach and embed concepts across the curriculum. • Where does my teaching fit in the program? • What can I rely on from previous instruction? • What’s viewed most important by the next grade level?
Cross Curricular Matrix - Vertical Surface Area & Area of Parallelogram & Triangle Find Area of Rectangles w/Formula Estimate Area of Rectangles
Cross Curricular Matrix - Horizontal Embedded Evaluating Expressions Surface Area & Area of Parallelogram & Triangle Embedded Order of Operations Pre-Teach Patterns & Multiplication Find Area of Rectangles w/Formula Embedded Multiplication Facts Pre-teach Adding & Estimating Estimate Area of Rectangles
Linear Measurement 5 in 4 in 12 in 3 in • Students are focused on addition • Perimeter is introduced as a tool to practice addition. • The triangle and rectangle have been covered since K.
New Polygons 6 ft 5 ft 4 ft 4 ft 5 ft 6 ft 30 ft • Addition Strategies • 5 + 6 + 4 + 5 + 6 + 4 • 5 + 10 + 5 + 10 • 5 + 5 + 10 + 10 • 10 + 20 • 30 ft Extension: 1 digit – 2 digit – 3 digit Missing sides (subtraction) Explicit word problems Strategic word problems Addition Properties
7 ft 7 ft 3 7 ft 21 ft No units? Why feet? 7 ft 9 ft 9 ft 9 ft 4 9 ft 36 ft 9 ft
12 squares 8 squares • Estimates are more common than “exact answers” • Estimates reveal understanding and/or gaps in conceptual understanding. 10 squares
4 4 1 4 squares 4 2 2 4 squares 5 5 1 5 squares 6 6 1 6 squares 6 2 3 6 squares 7 7 1 7 squares 8 8 1 8 squares 8 2 4 8 squares
1 24 squares 24 50 lines 24 2 24 24 squares 28 lines 12 3 24 24 squares 22 lines 8 4 24 24 squares 20 lines 6
4 Area = L x W Area = (4) x (3) Area = 12 Squares 3
A = A1 + A2 A = (L1 x W1) + (L2 x W2) A = (5 x 6) + (4 x 6) A = 30 + 24 A = 54 Squares 5 4 1 2 6 6
Activity • Use: • Standard Map • Grade Level Standards • Template for Curriculum Matrix • To • Develop curriculum matrix for angles.
Thank You Keith Smith 916-505-8835 keith@pacent.org
