K-5 EnVision Math At St. Michael’s School, students in grades K through 5 are taught using the EnVision math curriculum. EnVision Math requires students to make use of all Standards for Mathematical Practice – making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, constructing viable arguments and critiquing the reasoning of others, modeling with math, using appropriate tools strategically, attending to precision, looking for and making use of structure, and looking for and expressing regularity in repeated reasoning. Each EnVision math lesson includes multiple components:
1. A review that covers concepts previously taught
2. An interactive technology piece in which students get to watch a video, conduct “partner talks” with their classmates, solve problems, and respond to characters in the video, all while learning the new concepts for the current lesson
3. The introduction of the lesson presented through real-life situations
4. The current lesson, which engages students and gives them the opportunity to solve problems using previously-learned and new math concepts
5. An independent portion in which students are directed to complete the remainder of each math lesson independently, with a partner, or in a small group
The independent portion of each math lesson requires students to show their thinking by drawing, writing sentences, and/or modeling with math manipulative. This key piece, which requires students to reach one step beyond simply providing a number to answer a math problem, not only enhances students’ understanding of new and complex concepts, but it gives students the opportunity to think critically about their own work and the work of others. Kindergartners are able to explain their thinking using pictures they have drawn, while fifth graders learn to master the ability of making sense of problems and self-correcting as they problem solve. This key piece also encourages students to grow their “thinking stamina.” Students are presented with problems and want to solve them because they know that getting the wrong answer does not mean they have to give up due to a lack of understanding, but instead they have multiple tools that they can use to move one step closer to solving a problem.
Kindergarten Math in kindergarten encourages students to begin thinking independently. Students are encouraged to be brave thinkers, make smart guesses, and seek help from others when needed. Kindergarten math covers the topics of sorting and classifying, counting, comparing more and fewer, addition, subtraction, patterns, geometry, measurement, capacity and weight, time, graphing, and numbers to 30. Students in kindergarten also use math manipulatives to support their problem solving and model their thinking. These manipulatives include two-color counters, connecting cubes, two and three-dimensional shapes, tangrams, and number lines. Differentiated Instruction During math lessons, the classroom teachers and instructional aides work individually with students who require extra support. Teachers also work with small groups of students, as needed, to support their learning, challenge their thinking, and enhance their understanding in a setting that meets students’ specific needs. Additionally, the math resource teacher works with small groups of students to provide extra support for students who are struggling or added challenges for accelerated students.
Grade 1 In first grade, math lessons require students to work independently, collaborate with one another to solve problems, draw pictures and write to explain, seek help from the teacher, and make algebraic connections. First grade students learn to grow confident in making sense of math problems, using their writing skills to explain how they solve problems and talking about math with their classmates and teacher. First grade math covers the topics of addition, subtraction, number relationships, counting and number patterns, place value with tens and ones, numbers to 100, length, time, geometry, utilizing data, and fractions of shapes. Students in first grade also use math manipulatives to support their problem solving and model their thinking. These manipulatives include two-color counters, dice, connecting cubes, two and three-dimensional shapes, rulers, number lines, and card decks. Differentiated Instruction During the independent portion of math lessons, the classroom teacher and the math resource teacher work with small groups of students who need extra support and/or small groups of students who require an added challenge. In addition, each week during a math centers period, students are separated into groups based on their level of understanding of the current math concepts being taught. Teachers work with these small groups to support their learning, challenge their thinking, and enhance their understanding in a setting that meets students’ specific needs.
Grade 2 Math in second grade allows students to continue exploring multiple ways of solving problems, while challenging students to increase their thinking endurance and reasoning abilities. Second grade math covers the topics of addition and subtraction strategies, place value to 1000, mental math, addition and subtraction of two- and three-digit numbers, geometry, money, length, time, and using graphs and data. Students in second grade also use math manipulatives to support their problem solving and model their thinking. These manipulatives include two-color counters, dice, double dice (a small die inside of a large die), connecting cubes, three-dimensional shapes, clocks, number lines, card decks, rulers, and paper clips. Differentiated Instruction and Collaborative Work During math lessons, the math resource teacher works with small groups of students who need extra support and/or small groups of students who require an added challenge. In addition, each week during a math centers period, students are separated into groups to complete math tasks that review concepts introduced that week. Students collaborate with one another to solve problems and explore challenging concepts together. Teachers allow students to work independently, while also providing guidance as needed during this time.
Grade 3 Math in third grade requires students to explore relationships between numbers and operations, while continuing their progress in thinking critically to find and use multiple ways to solve problems. Third grade math covers the topics of numeration, using addition and subtraction to establish number sense, using place value to add and subtract, multiplication, division, fractions, geometry with two-dimensional shapes and their attributes, time, perimeter, area, liquid volume and mass, and recording and using data. Students in third grade use number tiles and fraction strips as math manipulatives to support their problem solving and model their thinking. Differentiated Instruction and Collaborative Work During math lessons, the math resource teacher works with small groups of students who need extra support and/or small groups of students who require an added challenge. In addition, each week during a math centers period, students are separated into groups to complete math tasks that review concepts introduced that week. Students collaborate with one another to solve problems and explore challenging concepts together. Teachers allow students to work independently, while also providing guidance as needed during this time. During this centers period, students may also spend time playing math games as a whole class and/or in their small groups. Additionally, students receive differentiated homework based on their current level of understanding of the math concepts being taught.
Grade 4 Students in fourth grade continue to make use of all mathematical practices, while extending their knowledge and familiarity with numbers and operations. Fourth graders are required to increase their thinking stamina, while learning how to use the math concepts they have mastered to solve new and challenging problems. Fourth grade math covers the topics of multiplication and division meanings and facts, generating and analyzing patterns, place value, addition and subtraction of whole numbers, multiplying by 1 and 2 digit numbers, dividing by 1 digit divisors, number sense and fluency with multiplication and division, fraction equivalence and ordering, adding and subtracting fractions, working with mixed numbers, measurement and conversion, problem solving with measurement and data, lines, angles, and shapes. Students in fourth grade use fraction strips, counters, and nets as math manipulatives to support their problem solving and model their thinking. Differentiated Instruction and Collaborative Work Math in fourth grade is taught in a small group setting, in which students are grouped based on their current level of understanding of the math concepts being taught (at grade level and accelerated). Small groups provide an environment for focused teaching to meet the needs of the students in each class. In addition, students may receive differentiated homework based on their current level of understanding of the math concepts being taught.
Grade 5 Students in fifth grade continue to make use of all mathematical practices, while extending their knowledge and familiarity with different types of numbers and increasingly complex operations. Fifth graders also prepare for middle-school math by learning how to effectively apply old and new math concepts to real-world situations. Fifth grade math covers the topics of place value, adding and subtracting decimals, multiplying whole numbers and decimals, dividing by 1- and 2- digit divisors, dividing decimals, numerical expressions, patterns, and relationships, adding and subtracting fractions and mixed numbers, multiplying and dividing fractions and mixed numbers, volume, units of measure, data, classifying plan figures, and coordinate geometry. Students in fifth grade use unit cubes, money, and nets as math manipulatives to support their problem solving and model their thinking. Differentiated Instruction and Collaborative Work Math in fifth grade is taught through leveled classes, in which students are grouped based on their current level of understanding of the math concepts being taught (at grade level and accelerated). Leveled classes allow teachers to work with smaller groups of students, providing an environment for focused teaching that meets each group of students’ specific needs. Students also receive differentiated homework based on their current level of understanding of the math concepts being taught.