• Grade 4 

    About Bridges in Mathematics 

    Bridges in Mathematics, second edition, is a comprehensive K–5 mathematics curriculum that equips teachers to fully implement the Common Core State Standards for Mathematics in a manner that is rigorous, coherent, engaging, and accessible to all learners. The curriculum focuses on developing students’ deep understandings of mathematical concepts, proficiency with key skills, and ability to solve complex and novel problems. Bridges blends direct instruction, structured investigation, and open exploration. The program taps into the intelligence strengths of all students by presenting material that is as linguistically, visually, and kinesthetically rich as it is mathematically powerful. 

    Bridges Activities 

    A Bridges classroom features a combination of whole-group, small-group, and independent activities that are problem centered. Fourth graders engage in five major kinds of activities:  

    • Problems & Investigations
    • Work Places
    • Math Forums
    • Problem Strings
    • Assessments 

    Problems & Investigations 

    Problems & Investigations are whole-group activities that also incorporate periods of independent and partner work. They often begin with a problem posed by the teacher, followed by time for students to think independently, work for a period of time, and talk in pairs before reconvening to share and compare strategies and solutions as a whole class. 

    Work Places 

    Work Places are engaging, developmentally appropriate math stations that offer ongoing practice with key skills. Many Work Places are partner games, but some are independent activities or more open-ended partner work. Work Places are always introduced and practiced as a whole class, after which students have opportunities to repeat the Work Place over a period of weeks. Work Places include suggestions that enable the teacher to differentiate each activity to address students’ needs for additional support or challenge. 

    Math Forums 

    Students discuss their solutions to and strategies for solving problems in nearly every Bridges lesson. Math forums, which occur a few times in most units, are a more formal and structured time for students to share and discuss their work. Prior to conducting a forum, the teacher reviews students’ written work on a particular problem and selects specific students to share during the forum. She carefully plans the order in which students will share to help the rest of the class develop a deeper understanding of the problem and the variety of strategies that can be applied to solve it. Students who are not sharing their own work are expected to listen carefully, compare their classmates’ work to their own, and ask questions to better understand each student’s ideas. 

    Problem Strings

     Problem strings are fast-paced exercises in which the teacher presents a carefully structured sequence of problems one at a time to the entire class. Each time, students solve the problem independently using any strategy they like, and then the teacher uses a specific model (a number line or ratio table, for example) to represent students’ strategies. The goal is to help students develop more efficient ways of solving a particular kind of problem, based upon the connections they see among the problems in the string. In Bridges Grade 4, problem strings are featured in Units 2, 4, and 6. 

    Assessments

     Assessments in Grade 4 are generally completed independently. Teachers have many opportunities, especially during Work Places, to make observational assessments of students working in small groups and to adjust the activity immediately based upon those observations. 

    Opportunities for work samples are also highlighted throughout the curriculum. 

    Number Corner 

    Number Corner is a skills program that is an essential part of the Bridges curriculum, but which can also be used to supplement any elementary math curriculum. This collection of quick daily skills activities makes use of a classroom display featuring a calendar, growing collections, number lines, and more. The display engages students and contributes to a math-rich classroom environment that promotes both procedural fluency and conceptual understanding. 

    Mathematical Emphasis 

    The mathematics in Bridges Grade 4 fully addresses the Common Core State Standards for fourth grade. The program is aligned to the Critical Areas of Focus and Major Instructional Shifts outlined by the authors of the CCSS. It weaves together the standards for content and practice in ways that support student learning. Bridges Grade 4 also features key visual models that deepen students’ mathematical learning while providing developmentally appropriate opportunities. 

    Content 

    Bridges develops children’s mathematical thinking and reasoning abilities through age appropriate problems and investigations in the areas of number, operations, algebraic thinking, measurement, data, and geometry. Some of these problems and investigations grow out of ventures into everyday life, while others delve more deeply into the world of mathematics itself.  Students are encouraged to explore, develop, test, discuss, and apply ideas: to see mathematics as something that is fluid, vibrant, creative, and relevant. 

    This year, students focus intensively on the three critical areas specified by the Common Core State Standards for Mathematics in Grade 4: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

     Bridges Grade 4 includes eight units of study, with 20 sessions per unit. Much of the work in Unit 1 provides students with opportunities to explore multiplication and division, focusing in particular on models, strategies, and multiplicative comparisons. During Unit 2, students continue to build multiplicative reasoning as they work with multi-digit multiplication and early division. Later in the year, during Unit 6, students revisit multiplication and division as they explore the many connections between the two. Each module in Unit 6 is rich with opportunities to model and solve problems, share and explain strategies, play games, and apply computational skills and concepts in a variety of contexts. 

    During Unit 3, students focus on fractions and decimals. They work with a variety of tools, including folded paper strips, egg cartons, geoboards, number lines, and base ten pieces, to model, read, write, compare, order, compose, and decompose fractions and decimals. In Unit 4, students study addition, subtraction, and measurement concepts. They compare the use of algorithms to other methods and make generalizations about which work best for certain problems. The measurement concepts in this unit include length and distance, liquid volume, time, mass, and weight. During Unit 5, students are formally introduced to a host of new geometric concepts, including angles and angle measure, parallel and perpendicular lines, and reflective symmetry. They also measure the area and perimeter of rectangles, making generalizations that support the introduction of the formulas for both skills and concepts into working with larger numbers and bigger ideas. Unit 7 offers a review of material covered earlier in the year, as well as opportunities to extend skills and concepts into working with larger numbers and bigger ideas. Early in the unit, students investigate a variety of shape and number sequences, looking for patterns that will enable them to extend each sequence and state the general rule that produced it. In the second module, they hone their skills at choosing and writing equations to represent multi-step number and word problems.In the latter half of the unit, they review some of the strategies they have developed for multi-digit multiplication over the year, and explore the standard multiplication algorithm.

     The final unit of the year uses science and engineering explorations to revisit and cement the mathematical skills students have built in the previous units while providing a foundation for work they’ll begin in fifth grade. Students design and build scaled model playgrounds that incorporate simple machines. They experiment with simple machines, conduct research to help them make decisions about safety issues, survey the school community to find the most important playground items to use in their designs, and use spreadsheet software to analyze the data they collect. They then use the information to create a scaled map of their designs and to build a scaled 3-D model. 

    Practices 

    The Common Core State Standards describe eight mathematical practices that characterize the ways in which mathematically proficient students engage with mathematical content. In Grade 4, students employ these practices with increasing independence, focusing in particular on improving their mathematical communication skills, modeling with mathematics, and reasoning both abstractly and quantitatively. 

    The broad characteristics of each practice in the fourth grade classroom are also described here. 

    CCSS Standard for Mathematical Practice

    Characteristics at Grade 4 

    Make sense of problems and persevere in solving them (4.MP.1)

    Fourth graders consider the meaning of a problem and look for appropriate, efficient ways to solve it. They use concrete and visual models as well as expressions and equations to represent, understand, and solve problems. They try different approaches when necessary, evaluate whether their solutions make sense in the context of the problem, and use alternative methods to check their answers. 

    Reason abstractly and quantitatively (4.MP.2)

    Fourth graders connect the specific quantity represented by a number to written symbols. They make abstract representations of problems as they solve them, for example by writing equations, but can also think about those symbols in relation to the problem to make sense of the quantities in context.

    Construct viable arguments and critique the reasoning of others (4.MP.3)

    Fourth graders refine their mathematical communication skills by using words (written and spoken) and symbols (equations and expressions) to clarify their thinking. They support the representations they have made with sketches or objects, and they explain and justify their own strategies and solutions. They also ask specific questions to better understand and evaluate other students’ reasoning.

    Model with mathematics (4.MP.4) 

    Fourth graders represent mathematical situations with numbers, words, sketches, actions, charts, graphs, equations, arrays, and ratio tables. They learn to connect these models and explain the connections among them. They use models not only as a way to represent problems, but also as tools for solving them and developing deeper understanding of the mathematics. 

    Use appropriate tools strategically (4.MP.5)

     

     

     

    Fourth graders learn to consider the tools, both concrete and abstract, at their disposal and to select the ones that will be most useful to them in solving a particular mathematical problem or performing a particular task. For example, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size of units within a system and express measurements given in larger units in terms of smaller units. To use tools strategically, students must understand the requirements of the task, their own needs and strengths, and the capabilities of the tools available to them.

    Attend to precision (4.MP.6)

    Fourth graders are increasingly able to be clear and precise in communicating mathematically, both in writing and in discussion. They specify units of measure and are careful to use the correct language to describe operations and symbols. They also take care to measure, draw, and label with precision.

    Look for and make use of structure (4.MP.7)

    When considering mathematical situations and solving problems, fourth graders seek out patterns and notice structure. They use what they notice to solve problems and develop deeper conceptual understandings.

    Look for and express regularity in repeated reasoning (4.MP.8) 

    Fourth graders notice repetition when solving problems and use that repetition to develop more efficient strategies for solving similar problems. Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms.

     *Retrieved on May 25, 2014 from http://bridges.mathlearningcenter.org/