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This presentation by Keith Smith from Pacent Learning Solutions focuses on innovative methods for teaching geometry across grades 3 to 5. It introduces a cross-curricular matrix emphasizing area and perimeter, along with sample lessons tailored for each grade. The agenda includes discussions on algebra readiness, time management in teaching, prioritizing essential concepts, and strategies for embedding geometry in various subjects. Attendees will learn how to create a cohesive curriculum that meets learning standards while maintaining conceptual understanding through effective lesson planning.
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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
