1 st What is mathematics?


 Silas James
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1 s 1 st What is mathematics? What is a number? How is math being discovered or invented? What should be learned in a math course? What should be learned about understanding numbers? What math knowledge should be learned by age 5? by age 10? NUMBER SENSE, CONCEPTS, & OPERATIONS Whole numbers, decimals, fractions reads, writes, and identifies whole numbers through millions reads, writes, and identifies fractions and mixed numbers with denominators including: 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 100, 1000 reads, writes, and identifies decimals through hundredths Compares and orders whole numbers, percents, decimals and fractions uses symbols (>, <, =) to compare numbers compares and orders whole numbers through millions using MA.A MA.A : Required: District Benchmark Version 1 August
2 s What does finding the value of a number (digit) mean? Why do we order numbers? How does knowing about decimals help us work with money? concrete materials, number lines, drawings, and numerals compares and orders commonly used fractions and decimals to hundredths using concrete materials, drawings, and numerals locates whole numbers and decimals on a number line Concrete and symbolic representations translates problem situations into diagrams and models using whole numbers, fractions, mixed numbers, and decimals to hundredths including money notation MA.A Equivalency uses concrete MA.A Version 1 August
3 s How do models and pictures help you understand equivalent numbers and values? materials to model equivalent forms of whole numbers, fractions, and decimals identifies equivalent forms of numbers including fractions knows that numbers in different forms are equivalent or nonequivalent using whole numbers, decimals fractions, and mixed numbers How does estimation, rounding, comparing, and ordering of whole numbers aid in problem solving? When would you use estimation? Uses estimation chooses, describes, and explains estimation strategies used to determine the reasonableness of solutions to real world problems estimates quantities of objects to 500 or more and explains the reasoning for the estimates (using compatible numbers, MA.A Version 1 August
4 s benchmark numbers, and unitizing) How can expanded forms of numbers help with understanding the value of the digits in a number? Uses placevalue concepts of grouping based upon powers of ten within a number system understands the value of a given digit in numbers from hundredths to millions including writing and interpreting expanded forms of numbers MA.A When would you use addition in your everyday life? How is it helpful to understand the Adds, subtracts, and multiplies explains and demonstrates the addition and subtraction of whole numbers and decimals (to hundredths) using concrete materials, drawings, story MA.A Version 1 August
5 s properties of addition? How can you use manipulatives to understand multiplication concepts? problems, and algorithms understands the properties of numbers including the following: the identity, commutative, and associative properties of addition How can finding factors and multiples of a number help you understand multiplication? What are prime and composite numbers? Prime numbers, composites, factors, and multiples knows factors and multiples of numbers to 100 multiplies by 10, 100, 1000 recognizing and demonstrating patterns knows divisibility rules for 2, 3, 4, 5, 6, 9, and 10 uses models to identify perfect squares to 100 explains and demonstrates the multiplication and MA.A Version 1 August
6 s How do patterns help you multiply 10 s, 100 s, and 1000 s? Why does it help to tell others how you solve problems? division of whole numbers and decimals (to hundredths) using concrete materials, drawings, story problems, and algorithms What do you feel is the best way to learn your multiplication problems? How are the number families of addition and subtraction like the relationship between multiplication and division? How important is it to learn your NUMBER THEORY Multiplication on whole numbers, decimals, and the effects of division on whole numbers recalls (from memory) basic multiplication facts and related division facts knows the inverse relationship of multiplication and division and demonstrates the relationship by writing related fact families MA.A Version 1 August
7 s multiplication tables by heart? How can knowing the multiplication facts help you in future math work? What does inverse relationship mean? understands the properties of numbers including the following: the identity, the zero, the commutative, associative, and distributive properties of multiplication predicts the relative size of solutions in the following: addition, subtraction, multiplication, and division of whole numbers addition and subtraction of decimals to hundredths explains and demonstrates the meaning of multiplication (for the repeated addition, array, and models) using manipulatives, drawings, number sentences, and story problems. Version 1 August
8 s How are multiplication and division related? When would you use division when you are among friends? Division explains and demonstrates division using concrete materials, drawings, story problems, and algorithms MA.A What can happen if you choose the wrong operations to solve real world problems? Selects operation(s) to solve addition, subtraction, multiplication, and division problems uses problemsolving strategies to determine the operation(s) needed to solve one and two step problems involving addition, subtraction, multiplication, and division of whole numbers and addition and subtraction of MA.A Version 1 August
9 s 2 nd How do you decide which strategy would be the best one to use for solving a given word problem? What type of strategy is your favorite to use to solve real world problems? When would you find a problem using decimals to the hundredths place in everyday life? NUMBER SENSE, CONCEPTS, & OPERATIONS decimals Solves real world problems using addition, subtraction, multiplication, and division solves and explains methods for solving real world problems involving addition, subtraction, multiplication, and division of whole numbers, and the addition and subtraction of decimals using the appropriate method (mental math, pencil and paper, or calculator) solves real world multiplication problems with whole numbers (3 digit by 1 digit) using concrete materials, drawings, and pencil and paper solves real world MA.A Required: District Benchmark Version 1 August
10 s How is the letter in an expression similar to a box, a question mark, or a blank in equations with missing information? How do models and manipulatives help you understand equalities and inequalities? ALGEBRAIC THINKING problems having divisors of one digit and dividends of three digits, with or without remainders solves real world problems involving the addition or subtraction of decimals (to hundredths) Solves problems involving equations or simple inequalities using manipulatives, diagrams, or models, symbolic expressions, or written phrases uses a variable to represent a given verbal expression (i.e. seven times a number = 7n) translates problemsolving situations into expressions and equations using a variable for the unknown MA.D Version 1 August
11 s How does understanding patterns help you understand relationships between numbers? Patterns and relationships describes, extends, and creates numerical and geometric patterns using a variety of models (lists, tables, charts) poses, solves, and explains problems by identifying predictable visual or numerical patterns (input/output) understands mathematical relationships in patterns (i.e. The second shape is the first shape turned 90 ) analyzes numbers, patterns, and states rules for relationships (2,4, 7, 9, 12, the rule is +2, +3, +2, +3, ) discusses, explains, and analyzes the rule that applies to the pattern MA.D MA.D Version 1 August
12 s applies the appropriate rule to complete a table or a chart (input/output) Uses models or graphs to solve equalities and inequalities uses physical or pictorial models or graphs (i.e. drawings, number lines) to solve equations or inequalities uses information from physical models, graphs, or tables to solve problems MA.D When would you need to put data into a table and graph? When would you choose to use various types of graphs? DATA ANALYSIS & PROBABILITY TABLES & GRAPHS understands the purpose of different parts of a graph (i.e. titles, labels, intervals, keys) chooses reasonable titles and labels for graphs MA.E Version 1 August
13 s How many examples of the different types of graphs can you find in magazines? Which type of graph would you use to show how you spend your time in a day? interprets and compares information from different types of graphs including graphs form contentarea materials and periodicals generates questions, collects responses, and displays data in a table, pictograph, circle, line, bar, or double bar graph interprets and completes circle graphs using common fractions analyzes and explains orally or in writing the implications of data displays Why might it be important to determine the mean of a series of numbers? Determines range, mean, median, and mode from sets of data identifies the mean, median, and mode MA.E Version 1 August
14 s from a set of data identifies the range on a line graph How can a calculator or computer assist you in the interpretation of a set of data? What makes creating graphs on a computer interesting? Analyzes real world data to recognize patterns and relationships of the measure of central tendency uses a calculator to determine the range and mean of a set of data uses computer applications to examine and evaluate data uses computer applications to construct graphs determines the number of possible combinations of given items and displays them in an organized way represents all possible outcomes for a simple probability situation or event using MA.E MA.E Version 1 August
15 s models such as organized lists, charts, or tree diagrams Predicts the likelihood of simple events occurring identifies and records, using common fractions, the possible outcomes of simple experiments using concrete materials (i.e. spinners, marbles in a bag, number cubes, coin toss) determines and predicts which outcomes are likely to occur and expresses those expected outcomes as fractions conducts experiments to test predictions MA.E Version 1 August
16 s 3 rd Why is it important to organize data? How can you use fractions to interpret information you get from experiments about probability? What different topics could you use to survey your classmates? Why do people survey other people? Why might you want to use a graph to display your information? Designs statistical experiments designs a class survey to collect data creates an appropriate graph to display data determines appropriate statistical measures for data explains the results using statistics (range and central tendency) Uses statistical data about life situations to make predictions and justifies reasoning uses statistical data to identify trends applies statistical data to make generalizations justifies and explains generations MA.E MA.E Required: District Benchmark Version 1 August
17 s When might you use a nonstandard unit of measurement? Why do we measure things in our world? What jobs do people use measurement tools to complete their work? MEASUREMENT Direct and indirect measures devises nonstandard, indirect ways to compare lengths uses customary and metric units to compare length, weight, and capacity uses multiplication or division to convert units of measure customary or metric MA.B Why is it important to use the correct measuring tool? What might happen if you tried to measure your book using yards? Measures length, weight, time, and temperature understands measurement concepts and can use oral and written language to communicate them knows about varied time intervals including decades, hours, minutes, and seconds selects and uses the appropriate tool for MA.B MA.B Version 1 August
18 s situational measures selects an appropriate measurement unit for labeling solutions to real world problems solves real world problems involving measurement using metric and customary units: length weight time capacity temperature angles uses schedules, calendars, and elapsed time to solve real world problems MA.B MA.B How do you determine whether you need to measure an object accurately or if estimation will do? and nonstandard units of measurement knows an appropriate unit of measurement to determine the dimension(s) of a given object knows an MA.B Version 1 August
19 s appropriate unit of measure (standard or nonstandard) to measure weight, temperature and capacity How does geometry depend on measurement in order to describe shapes? When might you need to estimate the area of a wall? Perimeter, area, and volume knows how to determine whether an accurate or estimated measurement is needed for a solution understands how to estimate the area and perimeter of regular and irregular polygons using graph paper, geoboard, or other objects understands how to estimate the volume of a rectangular prism using manipulatives or graphic representation MA.B Version 1 August
20 s When has your family had to solve real world problems using measurement? Why is it important to label your answer in a word problem? How can an artists use what they have learned about geometry in their artwork? GEOMETRY & SPATIAL SENSE Draws, describes, identifies, and analyzes 2 and 3 dimensional shapes uses appropriate geometric vocabulary to describe properties and attributes of 2 and 3dimensional shapes (faces, edges, vertices, diameter) draws and classifies 2 dimensional figures having up to eight or more sides MA.C How can you create a whole picture using just geometric shapes? Where could you find a picture that shows either symmetry, congruency, or reflections? Spatial relationships, symmetry, reflections, congruency, and similarity uses manipulatives to solve problems requiring spatial visualization knows symmetry, congruency, and reflections in geometric figures MA.C Version 1 August
21 s using drawings and concrete materials (pattern blocks, mirrors) knows how to justify that two figures are similar or congruent How does using manipulatives help you understand the reflections, translations, and rotations of figures? Flips, slides, or turns of a figure identifies and performs flips (reflections), slides (translations), turns (rotations 90, 180 ) using concrete and graphic materials (pattern blocks, geoboards, grid paper) knows the effect of a flip, slide, or turn (90, 180 ) on a geometric figure explores tessellations MA.C Geometric properties and formulas for 2 and Version 1 August
22 s 3dimensional shapes compares the concepts of area and perimeter using concrete materials and real world situations applies the concepts of area and perimeter to solve real world and mathematical problems knows how area and perimeter are affected when geometric figures are combined MA.C MEASUREMENT Measures perimeter, area, volume, angles understands measurement concepts and uses oral and written language to communicate them uses a wide variety of models and applies counting MA.B Version 1 August
23 s procedures to investigate measurements of length, areas, volume, and perimeter investigates angle measures using models and manipulatives for the common angles of 45, 90, 180 and uses these angles as reference points for measures of other angles GEOMETRY & SPATIAL SENSE MEASUREMENT Rectangular coordinate system understand how to identify, locate, and plot ordered pairs of whole numbers on a graph or on the first quadrant of a coordinate grid Estimates measurements including perimeter, area, and volume MA.C MA.B Version 1 August
24 s understands how to determine whether an accurate or estimated measurement is needed for a solution understands how to estimate the area and perimeter of regular and irregular polygons using graph paper, geoboard, or other objects understands how to estimate the volume of a rectangular prism using manipulatives or graphic representation How can number lines or diagrams help you understand functions? Solves real world problems (perimeter, area, capacity, volume, and angles) solves real world problems involving measurement using metric & customary units: perimeter MA.B Version 1 August
25 s NUMBER SENSE, CONCEPTS, & OPERATIONS area volume angles solves real world problems involving perimeter, area, and volume using concrete, graphic, or pictorial models to solve real world problems Common fractions reads, writes, and identifies fractions and mixed numbers with denominators including: 2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 100, 1000 locates fractions and mixed numbers on a number line explains and demonstrates the addition and subtraction of common fractions using concrete materials, drawings, story problems, and algorithms MA.A Version 1 August
26 s predicts the relative size of solutions in the addition and subtraction of common fractions When have you seen Roman Numerals in use? Roman Numerals uses concrete materials and symbolic notation to represent numbers in bases other than base ten, such as base five reads, writes, and compares the decimal number system to Roman numerals using: I, V, X, L, C, D, and M. MA.A th How do you decide which strategy would be the best one to use for solving a given word problem? NUMBER SENSE, CONCEPTS, & OPERATIONS Solves word problems uses problemsolving strategies to determine the operation(s) needed to solve one and two step problems involving addition, MA.A Required: District Benchmark Version 1 August
27 s What type of strategy is your favorite to use to solve word problems? How does the understanding of how to add, subtract, multiply, and divide smaller numbers help you when you solve problems using larger numbers? subtraction, and multiplication of fractions Adds, subtracts, and multiplies whole numbers, fractions, mixed numbers and decimals explains and demonstrates the addition and subtraction of common fractions using concrete materials, drawings, story problems, and algorithm solves real world problems involving the addition and subtraction of fractions using the appropriate method (mental math, pencil and paper, or calculator) predicts the relative size of solutions in the addition and subtraction of MA.A Version 1 August
28 s common fractions solves real world problems involving the addition or subtraction of common fractions with like or unlike denominators Prime numbers, composites, factors, and multiples knows divisibility rules for 2, 3, 4, 5, 6, 9, 10 uses models to identify perfect squares to 100 explains and demonstrates the multiplication and division of whole numbers and decimals (to hundredths) using concrete materials, drawings, story problems, and algorithms MA.A Version 1 August
29 s Division of larger numbers explains and demonstrates division using concrete materials, drawings, story problems, and algorithms MA.A Multiplication of larger numbers explains and demonstrates multiplication using concrete materials, drawings, story problems, and algorithms MA.A Version 1 August
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