Unit 1 - Place ValueStudents begin this course by exploring how to compose and decompose numbers with objects, with models, and with place value. They consider multiplication as repeated addition and learn multiplication math facts for the numbers three through nine. They investigate base-10 place value, as well as digits, values, periods, and expanded notation.Unit 2 - Rounding and ComparingNext students examine rounding on the number line to the nearest ten, the nearest hundred, the nearest thousand, and the nearest ten-thousand. They learn comparison symbols, comparing numbers up to 100,000, numbers in a table, and numbers in different directions. They discuss ordering numbers and identifying numbers with comparison clues.Unit 3 - Addition and Subtraction Part 1In this unit students study solving 1- and 2-step addition and subtraction problems with a model and with a number line. They learn the standard algorithm for addition and subtraction, with and without regrouping. They explore solving addition problems with three addends in an equation.Unit 4 - Addition and Subtraction Part 2Students use addition to solve for perimeter with known sides. They study subtraction with strip diagrams and practice combining before subtracting. They solve for an unknown side given perimeter. They are introduced to addition and subtraction with rounding. They count a collection of coins, a collection of bills and coins, and a collection of coins greater than $1.Unit 5 - Multiplication Part 1Next students count arrays, and learn to represent multiplication with arrays. They study the area of rectangles as arrays. They explore multiplication in a strip diagram, on the number line, and with skip counting. They investigate multiplication scenarios. They discuss the commutative and associative properties of addition and multiplication.Unit 6 - Multiplication Part 2In this unit students discuss the distributive property of multiplication. They learn to use distribution to multiply 2-digit by 1-digit numbers to arrive at products below and above 100. They multiply single-digit numbers by multiples of ten. They explore the standard algorithm for multiplying 1- and 2-digit factors to arrive at products below and above 100. They analyze multi-step multiplication, addition, and subtraction. They find rectangular area with inconsistent grouping.Unit 7 - DivisionStudents divide in a rectangular array, in groups of three, four, five, and six, and in an irregular array. They learn to double-double-double to multiply by eight, and to half-half-half to divide by eight. They divide in groups of seven, eight, and nine. They explore the power of knowing whether a number is even or odd. They find quotients using multiplication and divide with strip diagrams. They multiply and divide 11 on the 100s chart. They use multiplication to find a missing quotient, and use division to find a missing factor. Following this unit students are presented with the Mid-Term Review and Exam.Unit 8 - Multi-Step OperationsGoing on, students learn to find quotients and products in two steps. They study division and subtraction. They learn to choose operations based on whether the goal is to get bigger or smaller, and by whether they need the total or they have the total. They examine multiplication with money, stipends and bonuses, and how scarcity impacts cost. They also consider how borrowing money works.Unit 9 - FractionsIn this unit students compare fractions versus wholes. They learn to create fractions and unit fractions, and to use parts to make a whole. They add unit fractions and explore fractions on the number line. They share one item to create a unit fraction, make strip diagrams of fractions, and create polygon fractions. They find different paths to halfway, and use objects as fractions. They investigate equivalent fractions on the number line, with pictorial models, and with objects, and create equivalent fractions.Unit 10 - Comparing and Adding FractionsStudents compare two fractions with objects, with pictorial models, with the number line, and with words. They create greater and lesser fractions. They compare fractions in two different ways and create whole number fractions. They add unit fractions to create a whole.Unit 11 - TimeNext students learn to tell time to the hour, in increments of five minutes, and to the nearest minute. They add and subtract time, and tell time from analog to digital.Unit 12 - Geometry of 2D ShapesIn this unit students study polygons and quadrilaterals. Moving on to rectangles, they explore rectangular area and perimeter, and decompose rectangles to find area. They investigate squares, rhombuses, parallelograms, and trapezoids. They classify quadrilaterals. They analyze the pentagon and the hexagon. They discuss congruent polygons, including area and perimeter of congruent rectangles and congruent polygons with fractional area.Unit 13 - Geometry of 3D ShapesStudents examine 3D figures, including faces, edges, and vertices. They compare flat surfaces versus curved surfaces. Finally, they sort 3D shapes.Unit 14 - MeasurementNext students explore units of capacity. They measure liquid volumes. They learn relative units of customary and metric capacity, as well as customary and metric mass. They measure masses of objects and consider whether mass or liquid volume is appropriate. They practice addition, subtraction, multiplication, division, and problem-solving with mass and volume.Unit 15 - Paired Number TablesIn this unit students investigate paired number tables. They explore paired number tables with addition and with multiplication. They find the rule and the story of a paired number table.Unit 16 - Visual Representation of DataStudents study frequency tables, pictographs, dot plots, and bar graphs. They also learn to analyze each of these visual representations of data. Following this unit students are presented with the Final Review and Exam.
