How Our Curriculum Addresses

the Essential Academic Learning Requirements

 for Mathematics

1.1 understand and apply concepts and procedures from number sense number and numeration, computation, and estimation

Number and Numeration: Demonstrate understanding of integers, fractions, decimals, percents, place value of decimals, and properties of the rational number system using pictures and symbols.

• Students will use fractions, decimals, and percents to solve the four different activities: (a) calculating their bill at a restaurant, including tax, tip, and coupons (b) choosing items to buy based on their budget and minimal requirement, taking into consideration sales, percentages off, and sales tax (c) adapting a recipe – figuring out how to change a larger recipe for a smaller batch, and (d) deciding of equivalencies between fractions, decimals, and percentages in a relay race.

Number and Numeration: Compare and order integers, fractions, and decimals.

• Students will be presented with a variety of decimals and percentages in the relay game, and will need to decide what fraction(s) are equivalent.  This will require them to compare fractions, a few integers, and decimals.

Computation: Understand operations on nonnegative rational numbers.

·         Students will use addition, subtraction, multiplication, and division during all four of these activities.

Computation: Add, subtract, multiply, and divide nonnegative fractions and decimals using rules for order of operation.

• Students will add fractions and decimals in the relay race.  Students will multiply decimals in the restaurant and shopping activities.  Students will add, subtract, multiply, and divide fractions in the cooking activity.  They will be required to discuss how to solve these problems in regards to the orders of operation.

Computation:  Use mental arithmetic, pencil and paper, calculator, or computer as appropriate to the task involving nonnegative rational numbers.

• Students will have a variety of materials available to them, including mental mathematics, paper, calculators, Cuisenaire rods, and manipulatives.

Estimation: Use estimation to predict computation results and to determine the reasonableness of answers involving nonnegative rational numbers, for example, estimating a tip.

• Students will be asked to estimate a tip during the restaurant activity.

1.5 understand and apply concepts and procedures from algebraic sense  relations and representations, and operations

Representations: Use variables to write simple expressions, equations, and inequalities, for example, 3x > 18.

• Students will record their findings in their math journals, and will follow the procedure of writing their ideas in both informal registrar, and in mathematical registrar.  For some students, this will include expressing their thinking in algebraic notation.  Some students may not be ready for that step yet, however, and they do not need to do so in order to successfully complete the activities.

Operations: Solve single-variable equations.

• Students will record their findings in their math journals, and will follow the procedure of writing their ideas in both informal registrar, and in mathematical registrar.  For some students, this will include expressing their thinking in algebraic notation, and in solving their own algebraic, single-variable problems.  Some students may not be ready for that step yet, however, and they do not need to do so in order to successfully complete the activities.

2.2 formulate questions and define the problem

Identify missing or extraneous information.

• Students must decide for themselves how to solve these complex, real life word problems.  There is a great deal of information they will need to be able to shift through in order to complete these activities.

Define problems in new situations.

• Students will use similar skills to manipulate fractions, percentages, and decimals in four different scenarios.

Identify the known and unknown in new situations.

• Students will have to discover for themselves, in small groups, how to solve problems involving the manipulation of fractions, percentages, and decimals.  In order to do so, they will need to examine what information they know, and what information they need to complete these activities.

Organize relevant information from multiple sources.

• Students will be presented with a variety of options for how to complete four activities.  In the restaurant station, students have to use information for the menu, coupons, and their limited money to decide their meal, tax, and tip.  In the shopping station, students will have a variety of ads that offer a variety of sales, percentages off items, and will have to work within a budget to buy a minimum amount of specific items.  In the game station, students will have different ways to solve problems, and will have to decide which options work best for them.  In the cooking station, students will adapt a recipe to make a treat.

2.3 construct solutions by choosing the necessary information and using the appropriate mathematical tools

Select and use appropriate mathematical tools.

• Students will need to decide which mathematical tools to use to solve individual problems.  They will have a variety of materials available to them, including paper, calculators, Cuisenaire rods, and manipulatives.

Apply viable strategies and appropriate concepts and procedures to construct a solution.

• Students will use a variety of strategies to construct solutions, and will use the concepts of fractions, percentages, and decimals in their solutions.  They will record their findings in their math journals, and will follow the procedure of writing their ideas in both informal registrar, and in mathematical registrar.

3.1 analyze information from a variety of sources; use models, known facts, patterns and relationships to validate thinking

Compare, contrast, and interpret information from a variety of sources.

• Students will be gathering information from a variety of sale ads, and comparing and contrasting the prices of clothing, in order to decide how to most effectively use their budget.

4.1 gather information read, listen, and observe to access and extract mathematical information

Develop and follow a plan for collecting information.

• Students will develop a plan for how to use their $200 budget to buy school clothes.

4.2 organize and interpret information

Organize and clarify mathematical information by reflecting, verbalizing, discussing, or writing.

• Students will be asked to record their work in their math journals, and to discuss their strategies with their peers.

Explain or represent mathematical ideas and information in ways appropriate for audience and purpose.

·         Students will be recording their work, and reflecting on their strategies and experiences in their math journals after the activities.

5.1 relate concepts and procedures within mathematics recognize relationships among mathematical ideas and topics

Recognize the widespread use of mathematics in daily life and the extensive use of mathematics outside the classroom, for example, in banking or sports statistic

·         Students will use mathematics to calculate their bill at a restaurant, to buy school clothes, and to adapt a recipe.

5.3 relate mathematical concepts and procedures to real-life situations

understand the connections between mathematics and problem solving skills used every day at work and at home

Investigate the use of mathematics within several occupations/careers of interest.

·         Students will discover the necessity for understanding how to manipulate fractions, percentages, and decimals in (a) restaurant industry, (b) culinary arts, and (c) home economist.