Provincial Report Cards Mathematics Grades 1 to 12

Mathematics What does it mean to know and do mathematics in our classrooms? Think or write a few sentences about it. Discuss it with your colleague.

Making the Connections In order to link the curriculum to the report cards, it is necessary to examine what is the essence of the math curriculum. Reading the front matter of the curriculum is the place to start.

Questions to ask about the essence of mathematics curriculum: After perusing the front matter discuss some of the following questions with your colleague: What must a student know and be able to do to be mathematically literate? How do you encourage the understanding of the relationship between concrete, pictorial and symbolic representations of mathematics? What do you want your students to value about mathematics?

Goals for Students Mathematics is one way of trying to understand, interpret, and describe our world. The main goals of mathematics education are to prepare students to: confidently solve problems communicate and reason mathematically make connections to real life contribute to society as mathematically literate adults.

Instructional Focus Place emphasis on thinking/reasoning in mathematics Increase emphasis on problem-solving Develop number sense using mental math and estimation at every opportunity Incorporate oral and written communication in all areas of mathematics Emphasize conceptual understanding and connections within mathematics

Critical Components of the Curriculum The Math Processes Students focus on critical processes of the curriculum to build their understanding of mathematics to support lifelong learning. There are seven math processes in the curriculum. They represent the doing of math and permeate all the strands and are applied from Kindergarten to Grade 12. The processes are listed in the front matter of the curriculum.

Reasoning Technology Connections Visualization Mental Math and Estimation Problem Solving Communication Math Processes What does each of the processes involve? Click this picture to find out.

Math Processes All teaching and learning of mathematics in the curriculum involve students using these interrelated mathematical processes. These processes will serve students in all areas of their lives. They are life skills. The math processes support effective learning of mathematics and are considered to be essential to a balanced mathematics program.

Learning Activity Reflect, think and list: How are the processes demonstrated in your classroom? How are the processes evaluated? How do you ensure that the math processes permeate your teaching and students learning?

Making Connections The following categories infuse all grade levels. Knowledge and Understanding Mental Math and Estimation Problem Solving These categories are assessed and recorded on the Grades 1 to 8 report cards. Although these categories are to be emphasized, the Grades 9 to 12 report cards only record an overall percentage.

The Categories and Indicators for Grades 1 to 8 Report Cards Two of the seven processes are categories on the report card. The other five processes are embedded within all three of the categories. The categories and indicators are found on page 43 of the Manitoba Report Card Support Document and in the three slides that follow.

Knowledge and Understanding Indicators KNOWLEDGE AND UNDERSTANDING OF MATHEMATICAL CONCEPTS Student demonstrates knowledge and understanding of grade-specific mathematical concepts and skills in each strand ( number, patterns and relations, shape and space, statistics and probability) within each reporting period. -demonstrates knowledge and understanding of number, shape and space, patterns and relations, statistics - demonstrates knowledge and understanding of number, shape and space, patterns and relations, statistics and probability CATEGORYINDICATORS–GRADES 1 to 4INDICATORS–GRADES 5 to 8 This section describes what is meant by Knowledge and Understanding These sections show indicators respecting student achievement, performance and ability. Look at page 43 in your report card support document

Mental Math and Estimation Indicators MENTAL MATH AND ESTIMATION Student uses math knowledge and number facts to calculate mentally or estimate. -determines an answer using multiple mental math strategies -applies mental math strategies that are efficient, accurate, and flexible -makes a reasonable estimate of value or quantity using benchmarks and referents -uses estimation to make mathematical judgements in daily life -determines an answer using multiple mental math strategies -applies mental math strategies that are efficient, accurate and flexible -makes a reasonable estimate of value or quantity using benchmarks and referents -uses estimation to make mathematical judgements in daily life CATEGORYINDICATORS–GRADES 1 to 4INDICATORS–GRADES 5 to 8

Problem Solving Indicators PROBLEM SOLVING Student applies knowledge, skill, or understanding to solve problems. -applies various strategies to model solutions to problems -applies mathematical knowledge to solve problems -uses prior knowledge to connect math ideas to other concepts -uses appropriate technology to solve problems -uses visualization or models to demonstrate understanding -communicates problem-solving solutions by explaining his/her thinking -makes generalizations from patterns -applies various strategies to model solutions to problems -applies mathematical knowledge to solve problems -uses prior knowledge to connect math ideas to other concepts -uses appropriate technology to solve problems -uses visualization or models to demonstrate understanding -communicates problem-solving solutions mathematically -justifies mathematical thinking -thinks logically to make sense of mathematics (reasoning) -uses logic and divergent thinking to present mathematical arguments -applies algebraic reasoning when solving problems CATEGORYINDICATORS–GRADES 1 to 4INDICATORS–GRADES 5 to 8

Pictures of Practice Sample 1 – Imagine This: Number 12 The approved WNCP math resources for the curriculum provide a variety of examples of instruction and assessment. The following example comes from the teachers guide from Grade 1 Pearsons Math Makes Sense. (Unit 3 – Addition and Subtraction to 12, pages 40 and 62) Using the existing rubrics from the resource a correlation can be done with grade scale found on page 21 of the report card support document. Take a look at the sample and talk with your group. How does the sample compare to the report card categories and indicators? What other resources do you have that can work with the report card categories and indicators?

Sample 1: Imagine This: Number 12

Category 1 Knowledge and Understanding Category 2 and 3 Mental Math and Estimation Problem Solving Grade Scale: A correlation can be done with the grade scale descriptions found on page 21 of the report card support document.

Pictures of Practice Sample 2 – Jackson Video To watch video, click on the picture. Watch and listen to the strategies that the student uses. Look at Sample 2 which comes from the teachers guide Nelsons Math Focus Grade 4. (Teachers Resource Master Booklet Page 58.) Using the existing rubrics from the resource a correlation can be done with grade scale found on page 21 of the report card support document. Take a look at the sample and talk with your group. How does the sample compare to the report card category and indicators? What other resources do you have that can work with the report card categories and indicators?

Grade Scale: A correlation can be done with the grade scale descriptions found on page 21 of the report card support document. Category 2 Mental Math and Estimation

Pictures of Practice Sample 3 – Wrap It Up The approved WNCP math resources for the curriculum provide a variety of examples of instruction and assessment. The following example comes from the teachers guide from McGraw-Hill Ryerson Math Links 8, pages 627 – 629 and page 469 of the student textbook. Using the existing rubrics from the resource a correlation can be done with grade scale found on page 21 of the report card support document. Take a look at the sample and talk with your group. How does the sample compare to the report card categories and indicators? What other resources do you have that can work with the report card categories and indicators?

This describes the knowledge and understanding that the student will demonstrate.

Category 1 and 3 Knowledge and Understanding and Problem Solving

Grade Scale: A correlation can be done with the grade scale descriptions found on page 21 of the report card support document.

Pictures of Practice Sample 4 – Putting the Pieces Together This rubric was created by using the Grade 7 Math Support Document. It comes from the section, Putting the Pieces Together, page 65. It can be used at the end of a learning sequence for the strand, Patterns and Relations. Students have to create a book, graphic novel, or cartoon strip emphasizing patterns, their relations, and related vocabulary terms. In this investigation, students have the opportunity to demonstrate what has been learned in class. Take a look at the sample and talk with your group.

Teaching and Assessment The final grade for the report cards should be based on a variety of students evidence of learning. Assessment must be used as part of teaching and learning to help guide teaching and student learning.

Bibliography Manitoba Education. Kindergarten to Grade 8 Mathematics to Grade 8 Manitoba Curriculum Framework of Outcomes. Winnipeg, MB, Available on line at Manitoba Education. Grade 7 Mathematics Support Document for Teachers. Winnipeg, MB, Available on line at McGraw-Hill Ryerson. Math Links 8. Teachers Resource. Toronto, ON, McGraw-Hill Ryerson. Math Links 8. Student Textbook. Toronto, ON, Nelson. Nelson Math Focus 4 Teachers Resource Masters Booklet. Toronto, ON, Pearson Mathematics Makes Sense. Teacher Guide Unit 3: Addition and Subtraction to 12. Canada, 2007.