# Curriculum at a Glance Kindergarten- Grade 5

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1 Curriculum at a Glance Kindergarten- Grade 5 Students learn to reason and communicate, be problem-solvers, value mathematics and feel confident in their ability to apply concepts and skills. Creating such a foundation necessitates a well-articulated and developmentally appropriate program for all students. Elementary mathematics emphasizes conceptual understandings, multiple representations, deliberate connections and problem solving. The mathematical practices listed below are developed throughout the year. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Kindergarten Unit Name Content Numbers to 5 Count groups of 1, 2, 3, 4 and 5 Write the numerals 1, 2, 3, 4 and 5 Match and sort Look for sameness Understand not the same and different Sort using a single attribute Understand and spot differences Numbers to 10 Count from 1 to 8 Pair number names with numerals Introduce the concept of 0 Use 0 to 9 to tell the number of objects Read and write the numerals 1 to 9 Pair up sets of objects with other sets of the same quantity Introduce one more, one less, and the same number Pair up sets of objects one-to-one with other sets of the same quantity Order by Size, Length, or Weight Pair up sets of objects Order objects by size Use comparing words Order objects according to length and weight DPS

2 Counting and Numbers 0 to 10 Composing and decomposing numbers through 5 Pair number names with numerals Order numbers 0 to 10 Understand the concept of one more Know that fingers can represent a set of objects up to 5 Know that fingers and toes can represent a set of objects up to 20 Determine one more Understand and show the meaning of same and more, less and fewer Know how many more Use more and less to compare number values Size and Position Understand the concept of same-sized objects Explore the idea that only a few big objects fit into small spaces and many small objects fit into big spaces Identify positions of objects in space Use appropriate positional language to describe and compare Use language such as before or after to describe relative position in a sequence of events Numbers 0 to 20 Rote count to 20 Count 10 to 20 objects Read and write the numerals 10 to 20 Compare groups of up to 20 objects Order groups of up to 20 objects Solid and Flat Shapes Recognize and name basic 3-dimensional shapes Understand that some shapes have flat faces, edges, and corners and some do not Describe and name basic 3-dimensional and 2-dimensional shapes Recognize the relationship between 3-dimensional shapes and 2-dimensional shapes Draw 2-dimensional shapes Revisit big and small Identify basic 2-dimensional shapes within a scene Make a picture using basic 2-dimensional shapes Identify and extend a shape pattern Numbers to 100 Recognize and use pairs for counting Count by 2s Use the counting by 2s sequence to count up to 20 objects Count by 5s up to 20 Keep count of numbers using tallies Count by 10s Count by 1s to 49, 79, 100 Count from any given number to 49, 79, 100 Sequence numbers from 1 to 100 Comparing Sets Compare sets of up to 10 objects Understand more, fewer and less Compare sets of up to 20 objects Understand most and fewest Count the difference through comparing sets in one-to-one correspondence Count on DPS

3 Counting On and Counting Back Count on and back Revisit more and fewer Count on and back to find the difference between two sets Number Facts Compose numbers through 10 Decompose numbers through 10 Combine sets to make 5, 6, 7, 8, 9, and 10 Compose and decompose numbers to 20 with five-frames and ten-frames Count on using a number line Count on to find the difference Combine two sets to find how many more for sums through 15 Length and Height Compare lengths Use nonstandard units to measure and compare lengths Understand that more units are needed to measure a longer object than a shorter object Find differences in lengths using nonstandard units Understand tallest and shortest in terms of height Use nonstandard units to measure and compare heights Understand that more units are needed to measure a taller object than a shorter object Classifying and Sorting Classify objects using one attribute (color, size, shape, special features) Identify objects that do not belong to a set Classify objects according to two attributes and three attributes Sort objects by one or two attributes (color, size, shape, and special feature) Addition Stories Understand addition as the joining of two sets Understand symbols + and = and an equation Use symbols and numerals to write equations Represent addition stories with addition equations Fluency with addition facts to 5 Subtraction Stories Understand simple subtraction Understand the minus - symbol Use symbols and numerals to write equations Represent subtraction stories with subtraction equations Compare two sets and show the equation to answer how many more Fluency with subtraction facts to 5 First Grade Unit Name Content Numbers to 10 Count and compare numbers to 10 Count from 0 to 10 objects Read and write 0 to 10 in numbers and words Compare two sets of objects by using one-to-one correspondence Identify the set that has more, fewer, or the same number of objects Identify the number that is greater than or less than another number DPS

7 Solve one and two-step problems involving length Time Use the minute hand to show and tell the number for every five minutes after the hour Show and tell time in hours and minutes Use A.M. and P.M. to show morning, afternoon, or night Order events by time Graphs and Line Plots Read, analyze, and interpret picture graphs Read, analyze, and interpret tally charts, bar graphs, and line plots Make a line plot to show data Lines and Surfaces Recognize, identify, and describe parts of lines and curves Draw parts of lines and curves Identify, classify, and count flat and curved surfaces Identify 3-dimensional shapes that can stack, slide, and/or roll Shapes and Patterns Recognize and identify 2-dimensional shapes Combine and separate 2-dimensional shapes in figures Draw 2-dimensional shapes and figures on dot paper and square grid paper Recognize and draw shapes having a given number of angles Recognize and identify 3-dimensional shapes Build models using 3-dimensional shapes Combine and separate 3-dimensional shapes Identify and count the equal faces of a cube Third Grade Unit Name Grocery Stamps and Measuring Strips Content Use repeated addition Skip-count Double Use Partial Products Use Five-Times & Ten-times Doubles & Halves Surveys and Line Plots Organize, describe, interpret, graph, and categorical data pictorially Read and interpret a bar graph Use a line, bar graph, pictures to represent data Use a scale Describe using almost all, very few, half, more than half Describe the shape of data (spread, highest, lowest, outliers) Use data to compare groups Collections and Travel Stories Read, write, and order numbers to 1000 Use place value to determine the size of a number Make 3 digit numbers using 100 s, 10 s and 1 s Find pairs that add to 100 Subtract 3 digit numbers using parts, adding up, subtracting back DPS

8 Add 3 digit numbers by breaking apart and combining Add and subtract multiples of 10 and 100 Use number lines Visualize comparison and removal problems Telling time to the nearest 5 minutes Finding Fair Shares Naming, ordering unit fractions Identify equivalent fractional parts Use mixed numbers Identify halves and fourths in decimal and fraction form Express fractions in terms of area Combine fractions that sum to 1 Combine fractions into other fractions Telling time to a minute Solids and Boxes Distinguish polyhedra and non-polyhedra Distinguish pyramids and prisms Identify parts of polyhedra (faces, edges, vertices) and pyramids Design open boxes and nets for pyramids, cubes and other polyhedra Decompose 3D shapes and recombine them Determine the number of cubes that will fit in a box Muffles Truffles Use Repeated Addition Skip-count Use Partial Products Use Ten-times Double & Halve Perimeter Angles and Area Use US standard and metric units to measure length Find the perimeter of 2 D figures Create different shapes with the same perimeter Find the area of squares, triangles, and irregular shapes Use slides, flips, and turns to prove congruence between shapes Identify triangles and quadrilaterals Compare squares and rectangles Recognize right angles Compare size of angles Equal Groups Understand multiplying as combining groups and division as splitting into equal groups Use skip Counting, repeated addition, multiplication, arrays Writing and solving multiplication and division problems in context Finding multiples of 2,3,4,5,6, and 10 by skip counting Doubling and Halving Stories, Tables and Graphs Describe the shape of a line graph (increasing, decreasing, staying the same) Plot points on a graph Connect points on a graph, values in a table, and the situation it represents Compare situations by describing differences in graphs, differences in tables, Work with values that have a constant rate of change Identify the unit of a repeating pattern Extend number sequences with a constant increment Identify multiples of three DPS

10 Record and keep track of data Multiple Towers and Division Stories Multiply by breaking apart numbers, using arrays, diagrams Review multiplication combinations up to 12x12 Multiply multiples of 10 Solve division by making groups of the divisor and by using multiplication combinations. Find multiples of 2 digit numbers Find the product when the factor is doubled or halved Create story problems to represent a division expression Size, Shape and Symmetry Measure using US Standard and metric units Estimate lengths using cm, in, ft, yd, m Find the perimeter of objects Identify and classify polygons (especially quadrilaterals) using number of sides, length of sides, size of angles Combine polygons to make new polygons Identify a right angle as 90 degrees Measure acute angles Find the area of polygons by decomposing shapes Find the area of rectangles and triangles Make designs with line symmetry Box Factory Skip count Use partial products Use ten frames Double and halve Factor and group flexibly Penny Jars and Plant Growth Plot points on a coordinate grid Identify points on a grid with values in a table and the context it represents Describe steepness of a graph Compare rates of change in tables, graphs and situations between two quantities Write an arithmetic expression for finding one value in terms of another How Many Packages, How Many Groups Multiply multiples of 10 Solve 2 digit multiplication problems by breaking apart and making an easier problem Solve division problems by breaking the problem into parts and using multiples of 10 Fifth Grade Unit Name Number Puzzles and Multiple Towers Content Identify prime, square, even and odd numbers Find all the factors of a number Solve 2 digit by 2 digit multiplication problems by breaking up number and by multiples of 10 DPS

11 Solve division problems with 2 digit divisors by breaking up numbers and by multiples of 10 Use dot arrangements and arrays to model multiplication What s the Portion Fractions and Percents Field Trips and Fundraisers Thousands of Miles, Thousands of Seats -3) Decimals on Grids and Number Lines Use landmark unit fractions or common fractions Use decimal &/or percentage equivalents Use a ratio table as a tool to make equivalent fractions Use multiplication & division to make equivalent fractions Use a common whole to compare fractions. Read, write, and name the numbers and their relationships between 10,100,1,000 and 10,000 Add and subtract with large numbers using place value, the subtraction algorithm, and number lines Solve division problems related to multiplication combinations up to 12x12 Place decimals on a number line Identify fraction, decimal and percents that are equivalent Represent fractions as a part of an area Order decimals and compare to landmark numbers (0, ½, 1) Add decimals to the thousandths using place value reasoning Measuring Polygons Describe triangles using angle measures and lengths of sides Use angles to find other angle sin a polygon Compare perimeters and areas of rectangles Build similar figures Decompose and recombine 2D shapes What s the Portion Fractions and Percents Best Buys Use Partial Quotients Use Proportional Reasoning Use decimal or money sense Use a ratio table as a tool to make equivalent fractions Use x and to make equivalent fractions Use a common whole to add fractions Simplify to make a common whole Prism and Pyramids Decompose 3 D Shapes and recombine to make a given figure. Determine the volume of rectangular prisms, pyramids, cylinders, cones Use cubes to find volumes of larger figures. Comparing volumes as dimensions change Comparing volumes of different shaped containers Playgrounds Skip-count &/or use repeated addition to find a fraction of a whole Use multiplication & division to make equivalent relations Use landmark fractions to make partial products Use decimal &/or percentage equivalents Use a ratio table as a tool for making equivalent fractions Double & halve & the more generalized use of the associative property to eliminate fractions Use the standard algorithm for multiplication of fractions Interchange numerators (or denominators) to simplify first when multiplying DPS

12 Growth Patterns Use tables to represent the relationship between two quantities Plot points on a coordinate grid Compare and interpret graphs and tables Describe and compare steepness on graphs Write an arithmetic expression for finding one quantity in terms of another when using constant rates of change. Find a missing value given a constant rate of change Compare and describe graphs, tables, and situations for constant and non-constant rates of change How Long Can You Stand on One Foot Describe shape of data using spread, median, maximum, minimum, range, outliers Compare two sets of data using line plots and bar graphs Compare two sets of data using shape, spread, and medians Develop arguments and present conclusions based on data Design and carryout out an experiment to answer a question about two groups Compare the actual results of an experiment with the expected probability Express probability of possible outcomes DPS

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