What s So Singaporean About Geometry?
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1 What s So Singaporean About Geometry? Cassy Turner What is Geometry? Four Aspects of Geometry (Usiskin): Scan to find downloadable pages! 1. Visualization - Drawing and construction of figure 2. Study of the spatial aspects of the physical world 3. As a vehicle for representing non-visual mathematical concepts 4. Relationships and representation as a formal mathematical system (not in elementary school!) Representation: Measurement Measurement procedure: 1. Choose a standard unit. 2. Express measurements as multiples of that unit. 7 units of 8 ones = 56 ones 7 units of length 8 cm long 56 cm is how may units of 8cm? 6 units of 1/7m piece of fabric is a piece of fabric 6/7m long Teaching sequence (Parker & Baldridge): 1. a) Students directly compare objects according to their length, weight, etc. b) A simple non-standard unit is used to measure objects. c) A standard unit is introduced and students learn to read measurements along a scale. 2. Bigger and smaller standard units are introduced and students learn to convert between measurements expressed in different units. 3. In each step, students solve problems - both calculation problems and word problems. The problems are initially simple, and build to multi-step problems. Copyright 2013 Cassandra Turner
2 Measurement Topics - Length 1. b) Comparing with non-standard units: The unit is paper clips. How many paperclips tall is one bunny? Two bunnies? 1. c) Comparing with standard units - Grade 2 The unit is inches. How many inches tall is one bunny? Two bunnies? For more information, contact Cassy@SingaporeMathSource.com Page 2
3 2. Convert between measurements expressed in different units - Grade 3 Use outdoor chalk or tape in the gymnasium to mark 6 lines 1- meter apart on the floor. Have students take turns standing at the starting line and throwing a paper airplane. Measure the distance traveled by each plane in meters and centimeters. Whose plane travelled the longest distance? 3. Students solve problems - both calculation problems and word problems. 3 ft 7 in + 7 in = 4 ft 2 in 5 in 2 in 1 km m =? 1000 m m =? 1 km = 1000 m 1000 = hundreds 10 tens - 3 hundreds 5 tens 6 hundreds 5 tens Mr. Turner is 5 ft 10 in. tall. His son Cody in 6 ft. 3 in tall. How much taller is Cody than his dad? 5 ft. 10 in.? Mr. Turner Cody 6 ft. 3 in. For more information, contact Cassy@SingaporeMathSource.com Page 3
4 Measurement Topics - Weight Weight is a more challenging topic as you can t tell what an object weighs by looking at it. 1. b) Comparing with non-standard units: How many blocks does the bunny weigh? Which is heavier? 1. c) Comparing weight with standard units Grade 2 - reading scales 2. Convert between measurements expressed in different units - Grade 3 For more information, contact Cassy@SingaporeMathSource.com Page 4
5 3. Students solve problems - both calculation problems and word problems. 3 lbs 7 oz + 12 oz = 4 lbs 3 oz 9 oz 3 oz The total weight of a grapefruit and 5 tennis balls is 1 kg. If the weight of each orange is 60 g, find the weight of the grapefruit. 1 kg? 60 g Measurement Topics - Capacity 1. b) Comparing with non-standard units: 1. c) Comparing weight with standard units: Gallon Man: For more information, contact Cassy@SingaporeMathSource.com Page 5
6 Measurement Topics - Time It s not possible to compare non-standard units of time so the first two steps in the teaching sequence are skipped: Mommy will be home in 2 sleeps 1. c) Students learn to tell time with both an analog and digital clock. 2. Converting units of time 3. Solving problems for elapsed time: John took 45 minutes to ride his bike to the park. He left at 2:40. When did he arrive at the park? 10 minutes 10 minutes 10 minutes 10 minutes 5 minutes 2:40 2:50 3:00 3:10 3:20 3:25 Minnie watched a TV program that started at 8:30am and ended at 10:15 am. How long did the program last? 8:30am 9:00 am 10:00 am 10:15 am 30 minutes 60 minutes 15 minutes (1 hour) 30 min+60 min+15 min = 75 min The program lasted 1 hour 45 minutes. For more information, contact Cassy@SingaporeMathSource.com Page 6
7 Measurement Topic - Angles 1. a) Students directly compare objects according to their length, weight, etc. Join two strips of cardboard with a brad to form an angle maker Look for three angles around you and use your angle strips to compare them. 1. c) Comparing angles with standard units: For more information, contact Cassy@SingaporeMathSource.com Page 7
8 Geometric Topics - Shapes & Figures Two levels of identifying & drawing figures in a plane (2-d) 1. Sight recognition: a circle is a shape that looks like a circle. (Grades k-2) 2. Precise definition: a pentagon is a figure with five straight sides. (Grades 3 and up!) Names of parts: vertex side angle Triangles can be classified by both their angles: Acute, Right and Obtuse and their sides: Isoceles, Equilateral and Scalene Try this activity without measurement units first! Have students bring in straws to make the different types of triangles. If you use bendable straws, they can insert one end inside the other to make the triangles The CCSSM begins in grade 4 expecting students to: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. For more information, contact Cassy@SingaporeMathSource.com Page 8
9 Geometric Measurement Topic: Area Defining Area: 1. Fix a unit region and declare its area to be 1unit of area. 2. Express other areas of other regions as multiples of this unit area. Length is a number times a unit of length: 4 cm is 4 x 1cm Area is always a square unit. Why Square Units? An activity adapted from Parker & Baldridge Provide students with two room shapes and four different tile shapes: (Enlarge first!) A designer wants to compare the areas of two rooms in a house to see how many tiles she will need to cover the floor. The rooms need to be covered with identical floor tiles. Which shape tile will work best to cover these floors with no gaps? Squares and rectangles will fit the floors with no gaps. They Tesselate. Squares work better for defining area as smaller square tessellate larger ones. Practicing finding and filling an Area: Students need graph paper (inside a whiteboard is great!) Whole group version: volume. Two-player version: Two players on one board- take turns to roll the dice and filling in the area (use two different color markers). The first player who can t use their dice roll loses. For more information, contact Cassy@SingaporeMathSource.com Page 9
10 Geometric Measurement Topic: Volume Grades 1-3 focus on capacity. Volume of a liquid is easily measured as the capacity of a container. Grade 4 introduces volume of solids with the introduction of a unit cube. 1 cm connecting cubes. Have students create, then draw figures For more information, contact Cassy@SingaporeMathSource.com Page 10
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Contents TABLE OF CONTENTS Math Guide 6-72 Overview NTCM Standards (Grades 3-5) 4-5 Lessons and Terms Vocabulary Flash Cards 45-72
Contents shapes TABLE OF CONTENTS Math Guide 6-72 Overview 3 NTCM Standards (Grades 3-5) 4-5 Lessons and Terms Lesson 1: Introductory Activity 6-8 Lesson 2: Lines and Angles 9-12 Line and Angle Terms 11-12
An After-School Math Club Like No Other!
An After-School Math Club Like No Other! Any kid who likes math should get to enjoy more of it. So Bedtime Math has created Crazy 8s, a free kit that any school or public library can order to host an after-school
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Common Core State Standards Pacing Guide 1 st Edition Math Fifth Grade 3 rd Nine Week Period 1 st Edition Developed by: Jennifer Trantham, Laura Michalik, Mari Rincon ``````````````````````````````````````````````````````````````````````````````````````
What you'll need A measuring cup, 4 glasses of equal size, and water
Maths at Home Your home is full of opportunities to explore maths with your child and, at the same time, build his or her self-confidence and understanding of mathematical ideas. This is a chance for you
Correlation of USA Daily Math Grade 2 to Common Core State Standards for Mathematics
2.OA 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems with unknowns in all positions. 2.OA.2 Fluently add and subtract within 20 using mental strategies. 2.OA.3 Determine