Teaching Fractions using Visuals
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This document discusses using visual representations to teach fractions, including concrete objects like fraction discs and pictorial models. It recommends first building conceptual understanding before teaching procedural skills like computation. Key concepts covered include part-whole relationships, mixed numbers and improper fractions, multiplication and division of fractions using concrete examples, and word problems.
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The document outlines a schedule for four sessions occurring between 08:30-04:00 with a forum period from 03:30-04:00. It then discusses using a lesson on the Common Core to understand critical areas for Grade 1, including number bonds, comparison of numbers, and conservation of numbers. Various methods for developing visualization like the CPA approach, bar models, and teacher questioning are listed. The document goes on to discuss elements of effective math lessons including exploration, structure, journaling, reflection, and guided/independent practice using addition and subtraction strategies like counting all, making 10, subtracting from ten, and renaming before subtracting with examples provided.
Blake Grade 4
1) The document discusses standards and instructional focus areas for Grade 4 mathematics, including multi-digit multiplication and division, fractions, and geometric shapes.
2) It provides examples of case studies to solve, including arranging fractions in order and word problems involving fractions of amounts.
3) Theories of learning and representation discussed include Bruner's CPA approach and Skemp's classifications of understanding in mathematics.
Blake Grade 3
This document provides information about a grade 3 mathematics institute to be held on Wednesday. It discusses key theories in mathematics learning from Piaget, Bruner, Dienes, Vygotsky, and Skemp. The document also provides several case studies with examples of lesson plans and problems that assess different mathematical concepts like operations, fractions, problem solving, and place value.
Blake Grade 2
The document discusses a Grade 2 math institute that will focus on place value using concrete and pictorial representations. It provides several case studies on topics like subtraction across zeros, fractions, and problem solving. The lessons follow a basic format of an anchor task, guided practice, and independent practice. Key learning theories that will be drawn from include those from Piaget, Bruner, Dienes, Vygotsky, and Skemp. Bruner's CPA approach and Skemp's classifications of understanding will be particularly relevant for using different representations to build conceptual and relational understanding.
Blake Grade 1
Participants to Blake School Singapore Math Institute in June 2015 please download and print this set of handouts.
2104 WSU Cutouts
This document contains instructions for cutting out numbers and mathematical symbols from a page. It includes numbers from 0 to 9, basic mathematical operators like + and -, and instructions to cut out the listed items. The document is repetitive, listing the same numbers and symbols twice.
2014 WSU Handouts
The document summarizes discussions from breakout sessions at the 4th Singapore Math Institute on teaching mathematics using Singapore's approach. It provides tasks and problems from Singapore classrooms related to practicing skills through problem-solving, using anchor tasks to structure lessons, and teaching geometry in grades 4-6. The goals are to emulate Singapore's emphasis on problem-solving and multi-step word problems to develop students' mathematical thinking.
2014 WSU Day 2
The document discusses strategies for developing and improving mathematical practices, such as using anchor tasks, collaborative structures, questioning techniques, journals, textbooks for reflection, and focusing on visualization, generalization, and number sense. It also discusses moving from concrete to pictorial to abstract representations, and using anchor tasks and challenging word problems to teach Singapore math concepts.
2014 WSU Day 1 Slides
This document discusses using a problem-solving approach to teach mathematics. It focuses on practicing problem-solving lessons and breaking students into groups to work on problems. The document provides resources for lesson plans and contact information for the speaker who advocates for integrating problem-solving into mathematics education.
Se01 abc's of singapore math through whole numbers
The document discusses the Singapore approach to teaching mathematics, which was developed to help Singaporean students perform better in math. It is based on Bruner's ideas of a spiral curriculum and using representations. The document provides 15 sample math tasks that demonstrate fundamentals of Singapore Math instruction, such as the Concrete-Pictorial-Abstract approach. It also includes quotes from Bruner about revisiting basic ideas repeatedly to help students master structured bodies of knowledge.
Sd09 visualization
This document contains an agenda for a staff development conference on Singapore Math strategies with a focus on visualization. It includes 4 sample math tasks: 1) finding the area of a 4-sided polygon on a geoboard; 2) calculating leftover wire used to make a figure of 6 equilateral triangles; 3) dividing numbers by 3, 4, and 6; and 4) a word problem about Peter and Nancy exchanging coins to determine how many Peter originally had. The tasks are meant to illustrate ways to get students to visualize math concepts.
Sd02 challenge me
The document discusses strategies for differentiated instruction for advanced learners. It focuses on enrichment rather than acceleration. It provides 6 case studies as examples of anchor tasks that can challenge advanced learners in lessons, including problems about number sequences, geometry of rooms and chairs, properties of triangles, and finding sums of hexagon angles. The goal of the session is to explore general strategies for differentiating instruction to meet the needs of advanced students.
Sc02 fraction problems
This document contains a summary of fraction problems that will be covered in the "Let's Solve Them & Enjoy It: Fraction Problems" course at the Singapore Math Strategies National Conference. It outlines 7 fraction problems involving concepts like halves, adding fractions, finding percentages of amounts, and word problems about groups of children leaving a hall. The problems cover a range of skills from representing halves to multi-step word problems involving fractions.
2014 K-2 M4thodology Day 1
This document contains information from a presentation on developing number sense and problem-solving skills for grades K-2. It includes example math tasks and problems involving counting, addition, subtraction, and comparing quantities. Strategies are provided for using objects, pictures and diagrams to model word problems and develop conceptual understanding of part-whole and comparison situations. The document also lists questions to guide effective lesson planning and Polya's four-step model for mathematical problem-solving.
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- 1. Teaching Fractions Using Visuals Peggy Foo Marshall Cavendish Institute
- 2. Theories • Concrete-Pictorial-Abstract Approach pedagogical model • Enable students to visualize the concepts • Build conceptual understanding before we teach the skill of computation (procedural understanding)
- 3. Fractions • Represent a part-whole relationship • Need to provide ample opportunities to make sense of fractions using concrete, pictorial representation so that they can understand the abstract concept of fractions • Concrete materials– real objects, fraction discs, paper strips (folding) • Pictorial representations– model bars • Abstract - symbols and notions
- 4. Mixed Numbers and Improper Fractions • Watch a video
- 5. Multiplication of Fractions (Concrete) • Find the value of 1/2 x 2/3 • Find the value of ¾ x 2/3
- 6. Word Problem (Pictorial) • Tom spent 2/5 of his money on a shirt and ½ of the remainder on a pair of pants. What fraction of his money had he left?
- 7. Division by a whole number (concrete) • Share ¾ of a cake equally among 4 persons • What fraction of the cake does each person get?
- 8. Question? • Fraction ÷ Whole number = answer (smaller) • Fraction ÷ Fraction = answer (bigger or smaller?)
- 9. Division by a fraction (concrete) • Andrea wants to share 2/3 tub of ice-cream with his friends. She wants to give her friends 1/6 of a tub. How many friends can Andrea share the ice-cream with?
- 10. Challenging Word Problem
- 11. Summary • Using visuals to teach fractions to enhance conceptual understanding • Concrete (fraction discs, stripes) • Pictorial (bar model) • Abstract (symbols and notions)