We have so much to learn in math this year! We have many units that we'll progress through as the year goes along. Below is a highlight of each unit.
Unit 1: Whole Numbers/ Place Value In the first part of this unit, students will generalize their understanding of place value to 1,000,000, and understand the relative sizes of numbers in each place: They will recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Students will gain flexibility representing numbers in the different number forms. Students will gain place value understanding which extends beyond an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. In the second part of the unit, students build on their understanding of addition and subtraction, their use of place value and their flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place value in describing and justifying the processes they use to add and subtract. Students will solve multi-step story problems using addition and subtraction. Unit 2: Multiplication/Division Students will discover the meaning of prime and composite numbers. Students will generate multiple methods to multiply numbers* (i.e. base ten blocks, area models, partitioning, compensation strategies, etc.) and use words and diagrams to explain their thinking. They will use the terms factor and product when communicating their reasoning. Students will develop, discuss, and use efficient, accurate, and generalizable procedures to solve division problems with and without remainders. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. Students will apply multiplication and division strategies to solve problems. Unit 3: Fractions/Equivalence Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal and they develop methods for generating and recognizing equivalent fractions. Students will compare fractions by creating visual fraction models or finding common denominators or numerators. Students’ experiences should focus on visual fraction models (number lines, fraction bars or strips, area or length models) rather than algorithms. Students should learn to draw fraction models to help them compare.
Unit 4: Adding/Subtracting Fractions Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, and decomposing fractions into unit fractions. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. This unit provides a context for students to work with fractions by measuring objects to an eighth of an inch. Students are making a line plot of this data and then adding and subtracting fractions based on data in the line plot. Finally, This unit includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems.
Unit 5: Multiplying Fractions This unit builds on students’ understanding of adding fractions and extends that work into multiplication. Students are expected to use and create visual fraction models to multiply a whole number by a fraction, and understand multiplication as repeated addition. Students will use visual fraction models to solve word problems related to multiplying a whole number by a fraction. This unit also includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems. Examples of Word Problems: Kim runs 2/3 mile every day. How far does she run in one week? Ms Howard is making punch. The punch uses ¾ cup of orange juice for one serving. If she makes 8 servings, how many cups of orange juice does she need? Unit 6: Decimals Students will extend fraction and decimal understanding by changing fractions with a 10 in the denominator into equivalent fractions that have a 100 in the denominator. Students will make connections between fractions with denominators of 10 and 100 and the place value chart, and will read and write decimals. Students will use models (area models, decimal grids, decimal circles, number lines, and meter sticks) to compare decimals. This unit includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems. Unit 7: Geometry Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry. Students will classify two-dimensional figures using characteristics such as parallel or perpendicular lines or by angle measurement.
Unit 8: Measurement Students will solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Students are expected to use formulas to calculate area and perimeter of rectangles, and to communicate their understanding of why the formulas work. Students will identify, measure, and draw angles. This unit includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeter, dollars to cents). Students should have ample opportunities to use number line diagrams to solve word problems.
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