Fifth Grade Math

In this section: Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade Introductory Algebra 8th Grade Algebra Math Lab

Curricular Overview

The mathematics curriculum and pedagogy at San Francisco Day School is based on the belief that all children have fundamental attitudes of curiosity and the willingness and ability to probe, explore, experiment, make conjectures, and persevere with a piece of demanding work. The program is predominately Socratic in its execution and assists students in making connections between mathematical principles. Students are encouraged to use and understand a variety of methods and ideas in their mathematical applications and solutions.

Students begin the year with a thorough review of place value, addition and subtraction of large numbers, and basic multiplication facts. They also explore different bases, and are introduced to division as the inverse of multiplication, area and perimeter, and circle and bar graphs. Multiplication of 2- and 3-digit factors, using partial products and various algorithms, is practiced extensively, moving from the concrete to the abstract. Problem solving and logic, based on foundations put in place in fourth grade, continue to be studied.

The second semester begins with a study of metric and U.S. standard measures of length, distance, weight, and measures of time. Properties of two-dimensional shapes are measured by using perimeter and area. Students explore these concepts first with manipulatives and soon move to paper to tackle problems. Time is also spent exploring the concept of division. Again turning to manipulatives, students acquire an understanding of what division is and how the operation is used. Once this conceptual understanding is solidified, they work their way to the long-division algorithm. They then move on to a thorough unit on fractions. Once students understand the definition and function of a fraction, they are exposed to the ideas of equivalent fractions, improper vs. mixed numbers, fraction inequalities, the addition and subtraction of fractions, and ultimately, changing fractions into decimals and percents. Throughout the year, students are challenged by word problems, real-life problem-solving situations, and logic puzzles, which ask them to take the aforementioned concepts a step further.

As an ongoing year-long project, fifth-grade students explore math by living a simulated adult life complete with job, salary, taxes, expenses, etc. They develop number sense, calculation skills, and work with decimals and fractions throughout this unit. Computer lab visits supplement "Real Life" by helping students shop for groceries, purchase cars with several pay plan options, research and plan for vacations, explore investment options, and even purchase socially-responsible holiday gifts.

Goals and Objectives

Number and Operations

Addition and subtraction

• Continue to develop automatic recall of basic number facts
• Further practice with adding and subtracting numbers of several digits of the same or varying lengths

Multiplication and division

• Multiply 2- and 3-digit factors by (a) building and recording with base blocks, (b) partial products method, (c) algorithms
• Divide multi-digit dividends by one or two digit divisors using various algorithms
• Check solutions of division and multiplication problems using inverse operation
• Understand the relationship of division and multiplication shown by area arrays
• Understands the relationship of division and multiplication shown by area arrays
• Learn to interpret the remainders in division problems
• Select and use an appropriate method of calculation -- estimation, mental arithmetic, paper and pencil, or a calculator -- according to the nature of the problem
• Develop the ability to thoroughly explain and analyze methods and solutions verbally and in writing

Fractions

• Understand the concept of a fraction and its relationship to the whole
• Develop an understanding of equivalent fractions
• Identify fractions in the context of real life applications
• Compare, order, and combine fractions

Decimals

• Understand the concept of a decimal and its relationship to the whole
• Write or identify decimals from various concrete and visual models
• Read and write decimals through thousandths
• Practice adding and subtracting using decimals both by building and computation
• Compare and order decimals
• Rename decimals as fractions and percents

Percents

• Understands the concept of percent as "out of 100" or "100ths"
• Identifies the percent of a shaded region divided into 100 squares
• Identifies common equivalent expressions (decimals, percents, and fractions), and explains why they are equivalent

Numeration

• Identify and understand the place value in multi-digit numbers
• Read and write multi-digit numbers
• Develop the ability to round numbers
• Add and subtract money and round the result into appropriate units
• Explore other bases using concrete materials
• Use estimation to determine logical problem solving outcome

Measurement

• Be able to use standard linear measurement including customary and metric
• Understand properties of two-dimensional shapes such as perimeter and area

Geometry and Spatial Sense

• Understand mathematical terms such as a point, segment, ray, and line
• Explore similarity, congruency, and symmetry
• Identify lines as horizontal, vertical, diagonal, intersecting, parallel, and perpendicular
• Classify and construct various polygons using concrete models

Patterns and Functions

• Find the missing number in patterns using sums, differences, or products
• Read and interpret various graphs, tables, and charts

Data Analysis and Probability

• Predict, perform, and record results of simple probability experiments using fractions
• Interpret data, using average, median, mode, and range
• Collect data using observations, surveys, and experiments
• Represent data using tables and graphs such as line plots, bar graphs, and line graphs

Algebra

• Use variables in algebraic expressions to represent arithmetic relationships and represent basic properties of numbers
• Evaluate simple formulas
• Evaluate expressions that contain parentheses

Assessment and Evaluation

The fifth-grade teachers assess students throughout the year using pre- and post-assessments, ongoing individual evaluation of classwork, homework, cooperative group work, and teacher-created end-of-unit assessments.

Materials

Place value blocks
Base blocks
Color cubes
Color tiles
Decimal cards
Fraction bars
Fraction circles
Fraction tiles
Geoboards
Geometric solids
Pattern blocks
Pentominoes
Tangrams

References and Resources

Curriculum and Evaluation Standards for School Mathematics. NCTM, 2000.

Everyday Mathematics, 5th Grade. The University of Chicago Mathematics Project, 1999.

Get-it-Together: Math Problems for Groups, Grades 4-12. Equals Publications, Lawrence Hall of Science, 1989.

Groundworks: Algebra Puzzles and Problems, Grade 5 Creative Publications, 1998.

Investigations in Number, Data, and Space, as developed at the Technical Education Research Center. Creative Publications, 1987.

Lane County Math Project: Problem Solving in Math, Grade 5. Dale Seymour Publications, 1983.

Math Trailblazers: A Mathematical Journey Using Science and Language Arts, Grade 5. Kendall Hunt Publishing Company, 2003.

The Problem Solver 5: Activities for Learning Problem-Solving Strategies. Creative Publications, 1987.