Bridges in Mathematics is a comprehensive K–5 mathematics curriculum that equips teachers to fully implement the Common Core State Standards for Mathematics (aligned to AERO) 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. A Bridges classroom features a combination of whole-group, small-group, and independent activities that are problem centered.
First graders focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade 1: addition and subtraction within 20; whole number relationships and place value; linear measurement in non-standard units; and reasoning with shapes and their attributes. Students model, solve, and pose a wide variety of story problems to construct meaning for the operations of addition and subtraction, as well as an understanding of how the two operations are related. They extend the counting sequence to 120 and think of 2-digit whole numbers as groups of tens and ones. Students also develop, discuss, use, and generalize methods for accurately and efficiently adding within 100 and subtracting multiples of 10. Students are challenged to identify, describe, construct, draw, compare, compose, and sort shapes. They also learn about fractions in the context of two-dimensional shapes.
Second graders focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade Two: extending understanding of base ten notation; building fluency with addition and subtraction; using standard units of linear measure; and describing and analyzing shapes. Students learn to count by 5s, 10s, and multiples of hundreds, tens and ones; read, write, and compare numbers to 1,000; and develop fluency with addition and subtraction to 100 as they solve and pose a wide variety of story problems. They build foundations for understanding area, volume, congruence, similarity, and symmetry, which are explored in greater depth in later years. Students estimate and measure in inches, feet, yards, centimeters, and meters; and solve problems that involve adding, subtracting, and comparing lengths.
Third graders focus intensively on the four critical areas: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; and describing and analyzing two-dimensional shapes. Students learn to round whole numbers to the nearest 10 or 100. They apply this skill to estimating the results of multi-digit problems while developing increasingly efficient methods—including use of the standard algorithms—for adding and subtracting within 1,000. Students work with several models, including groups of equal sizes, the number line, and rectangular arrays, as they transition from additive to multiplicative thinking. Students work with fractions, measurement and estimation of time, mass, and liquid volume.
Fourth graders engage in five major kinds of activities: Problems & Investigations, Work Places, Math Forums, Problem Strings, and Assessments. 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. 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: developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; 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.
Fifth graders focus intensively on the three critical areas: developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and developing understanding of volume. Students use the study of volume to review and extend a host of skills and concepts related to multiplication. They use expressions with parentheses to represent different rectangular prisms, find the surface area of boxes, develop multi-digit multiplication strategies to solve real-world and mathematical problems, and revisit multiplication and division through the lens of the area model. Students learn to add and subtract fractions with unlike denominators, using a variety of strategies to find common denominators. They read, write, and compare decimals as well as round and examine the decimal patterns of multiplying and dividing numbers by 10. Students use their place value understandings to convert within a measurement system, and add and subtract decimals to hundredths.