Alburnett Community School 4 th Grade Mathematics Curriculum Map Unit 1 Numeration 2 Weeks

Transcription

1 4 th Grade Mathematics Curriculum Map Unit 1 Numeration or Understandings The base ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value. Numbers can be used for different purposes, and numbers can be classified and represented in different ways. Numbers can be approximated by numbers that are close place-value rounding Round numbers to the nearest 1,000,000. Compare and order whole numbers to 1,000,000. Identify and write numbers to 1,000,000. Unit 1 pretest End of unit test Online teacher resources from envisionmath 1

2 Unit 2- Adding and Subtracting Whole Numbers or Understandings Any number, measure, numerical expressions in equivalent forms can make some calculations easy to do mentally. Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. estimating problem solving adding whole numbers subtracting whole numbers subtracting across zeros Subtract with zeros to the thousands place Estimate sums and differences using rounding rules to the nearest 1,000. Unit 2 pretest End of unit test Online teacher resources from envisionmath 2

3 Unit 3: Multiplication Meaning and Facts or Understandings There are multiple interpretations of addition, subtraction, multiplication and division or rational numbers. Each operation is related to other operations. For a given set of numbers, there are relationships that are always true called properties and these rules govern arithmetic and algebra. Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. factors multiplication properties breaking apart partial products Apply multiplication properties to help find products. Identify multiplication as repeated addition. Recognize patterns for multiplication facts. Multiplication games from Nimble With Numbers Online multiplication games at Unit 3 pretest End of unit test Online teacher resources from envisionmath Nimble With Numbers (Grades 4 & 5) 3

4 Unit 4- Division Meanings and Facts Multiplication and division have an inverse relationship. The relationship can be used to find division facts; every division fact has a related multiplication facts Equal Groups Repeated Addition vs. Subtraction Division as Repeated Subtraction Division as sharing Use fact families to relate multiplication and division facts. Divide by 0 and 1. Find division basic facts by using multiplication facts. Use pictures, words, and numbers to represent sharing situations and find quotients. Multiplication/Division games from Nimble With Numbers Online multiplication games at Unit 4 pretest End of unit test Online teacher resources from envisionmath Nimble With Numbers (Grades 4 & 5) 4

5 Unit 5- Multiplying by 1-Digit Numbers 4 th Grade There is more than one way to do mental calculations involving multiplication. Different numerical expressions can have the same value. Or, the value of one expression can be less than, or greater than, the value of the other expression. Basic facts and place-value patterns can be used to find products when one factor is 10 or 100. Multiplying Multiples of 10 and 100 Recording Partial Products Rounding/Estimating Find products mentally using compatible numbers or breaking apart. Estimate products using rounding Use expanded algorithm to multiply Multiply 2-digit by 1-digit numbers Multiply 3-digit by 1 digit numbers Multiplication/Division games from Nimble With Numbers Online multiplication games at Unit 5 pretest End of unit test Online teacher resources from envisionmath Nimble With Numbers (Grades 4 & 5) 5

6 Unit 5- Multiplying by 1-Digit Numbers 4 th Grade or Understandings There is more than one way to do mental calculations involving multiplication. Different numerical expressions can have the same value. Or, the value of one expression can be less than, or greater than, the value of the other expression. Basic facts and place-value patterns can be used to find products when one factor is 10 or 100. Multiplying Multiples of 10 and 100 Recording Partial Products Rounding/Estimating Find products mentally using compatible numbers or breaking apart. Estimate products using rounding Use expanded algorithm to multiply Multiply 2-digit by 1-digit numbers Multiply 3-digit by 1 digit numbers Multiplication/Division games from Nimble With Numbers Online multiplication games at Unit 5 pretest End of unit test Online teacher resources from envisionmath Nimble With Numbers (Grades 4 & 5) 6

7 Unit 6 Patterns and Expressions Patterns can sometimes be used to identify a relationship between two quantities. Some mathematical phrases can be represented using a variable in an algebraic expression. Variables and Expressions Addition and Subtraction Expressions Multiplication and Division Expressions Recall the definitions of expression, ordered pair, factors, and multiple. Describe and analyze patterns Use multiplication to solve problems. Nimble With Numbers Unit 6 Pretest Nimble with Numbers Grades 5&6 7

8 Unit 7 Multiplying by 2-Digit Numbers Basic facts and place-value patterns can be used to mentally multiply a two digit number by a multiple of 10, 100, or 1,000. Rounding and substituting compatible numbers are two ways to estimate products. The expanded algorithm for multiplying by two-digit numbers is an extension of the algorithm for multiplying with one-digit numbers. Using mental math to multiply 2-digit numbers. Estimating products. Arrays and expanded algorithms Multiplying 2-digit numbers by multiples of ten. Multiplying 2-digit by 2-digit numbers. Use mental math to multiply by multiples of 10 or 100. Estimate products using rounding and compatible numbers. Use and array or expanded algorithm to multiply Multiplying two-digit numbers by multiples of 10. Multiplying two-digit numbers or grater Nimble With Numbers Unit 7 Pretest Nimble with Numbers Grades 5&6 8

9 Unit 8 Dividing by 1-Digit Numbers or Understandings Basic facts and place-value patterns can be used to divide multiples of 10 and 100 by one digit numbers The relationship between multiplication, division, and estimation can help determine the place value of the largest digit in a quotient The remainder when dividing must be less than the divisor Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers Estimating quotients Dividing with remainders Connecting models and symbols Dividing 2 and 3 digit numbers by 1 digit Deciding where to start dividing Factors Prime and composite numbers Divide three-digit by one digit numbers Determine the size of a quotient before dividing Find factors of a number Determine whether a number is prime or composite Solve multi-step problems Unit 8 Pretest 9

10 Unit 9 Lines, Angles, and Shapes Point, line, and plane are the core attributes of space objects and real world situations can be used to think about these attributes. Polygons can be described and classified by their sides and angles. Plane shapes have many separate properties that make them different from one another. The unit for measuring the size of the opening of an angle is 1 degree. Line segments and rays are sets of points. Points, Lines, and Planes Line Segments, Rays, and Angles Measuring Angles Polygons, Triangles, Quadrilaterals Identify and describe points, lines, and planes. Identify and describe line segments, rays and angles. Measure angles. Identify and describe polygons, triangles, and quadrilaterals. Unit 9 Pretest 10

11 Unit 10 Understanding Fractions A fraction describes the division of a whole into equal parts and is relative to the size of the whole. Benchmark fractions can be used to estimate fractional amounts. or Understandings A fraction can be expressed in its simplest form by dividing the numerator and denominator by factors until there are no other factors than 1. Fractional amounts greater than 1 can be represented using a whole number and a fraction. If fractions have the same denominator, the fraction with the greatest numerator is the greater fraction. If they have the same numerator, the fraction with the lesser denominator is the greater fraction. Regions and Sets Fractions and Division Estimating Fractional Amounts Equivalent Fractions Fractions in Simplest Form Improper Fractions and Mixed Numbers Ordering Fractions Comparing Fractions Identify and draw fractional parts of a region or parts of a set. Relate division to fractions. Estimate fractional parts of a region. Find equivalent fractions. Find fractions in simplest form Unit 10 Pretest 11

12 Unit 12 Understanding Decimals or Understandings Decimal numeration is just an extension of whole number numeration. Place value can be used to compare and order numbers. A decimal is another name for a fraction. Each fraction, mixed number, and decimal can be associated with a unique point on a number line. Decimal place value Comparing and ordering decimals Fractions and decimals Mixed numbers and decimals Read and write decimals through hundredths Compare and order decimals Relate decimals to fractions Locate and name fractions, decimals, and mixed numbers on a number line Unit 12 Pretest 12

13 Unit 13 Operations With Decimals Rounding decimals is a process for finding the multiple of 0.1, 0.01, etc., closest to a given number Techniques for estimating calculations with whole numbers can also be used to estimate calculations with decimals Multiplying a whole number by a decimal is similar to multiplying two whole numbers Dividing a decimal by a whole number is similar to dividing two whole numbers The relationship between addition and subtraction and between multiplication and division can be used to solve some equations Rounding decimals Estimating sums and differences of decimals Adding and subtracting decimals Multiplying a whole number and a decimal Dividing a decimal by a whole number Round decimals Estimate sums and differences of decimals using rounding Model adding and subtracting decimals Add and subtract decimals Multiply a whole number and a decimal Divide a decimals by a whole number Unit 13 Pretest 13

14 Unit 14 Area and Perimeter The amount of space inside a shape is its area and area can be estimated or found using square units The area of some irregular shapes can be found by breaking apart the original shape into other shapes for which the areas can be found The distance around a figure is the perimeter There are relationships between the perimeter and area of a polygon Area can be estimated in square units Understanding area Area of squares and rectangles Area of irregular shapes Area of a parallelogram Area of triangles Perimeter Same perimeter, different area Same area, different perimeter Estimate or find the area of a polygon on a grid Find the area of squares, rectangles, parallelograms, and triangles Find the perimeter of an object Compare rectangles with the same perimeter or area Use a table and solve a simpler problems Unit 14 Pretest 14

15 Unit 15 Solids Three-dimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces, edges, and verticies. Many every day objects closely approximate standard geometric solids. Some solids can be shown as a plane shape made up of other shapes. Vies of solids from different perspectives can sometimes be used to completely describe the solid Volume is the amount of space inside a sold figure. Solids Views of solids: Nets Views of solids: Perspective Volume Identify and describe solids Identify nets Identify two-dimensional views of solids Find volume of solids Unit 15 Pretest 15

16 Unit 16 Measurement, Time and Temperature Length can be measured in different systems and using different units in each system that are related to each other Capacity is a measure of the amount of liquid a container can hold The weight of an object is the measure of how heavy an object is Mass is a measure of the quantity of matter in an object. Weight and mass are different measures Time can be expressed using different units that are related to each other Temperature can be expressed using degrees and temperature change can be found using addition and subtraction Customary units of length Customary units of capacity Units of weight Changing customary units Using metric units of length Units of mass Changing metric units Units of time Elapsed time Temperature Estimate mass in metric units Convert metric units Compare units of time Solve problems involving elapsed time Read a thermometer and find changes in temperature Unit 16 Pretest 16

17 Unit 17 Data and Graphs Each type of graph is most appropriate for certain kinds of data Some questions can be answered using a survey. There is more than one way to describe the center or typical number in a numerical data set Data from surveys Interpreting graphs Line plots Ordered pairs Line graphs Mean, median, mode, and range Stem and leaf plots Circle graphs Organize and interpret data from surveys Interpret bar graphs Interpret line plots and identify outliers Name and locate ordered pairs on a coordinate grid Read and interpret line graphs Find mean, median, mode and range Unit 17 Pretest 17

18 Unit 18 Equations Two algebraic expressions are equal if the value of each expression is the same when each variable is replaced with its assigned number and the resulting calculations are completed A solution to an equation is a value of the unknown that makes the equation true. A solution to an inequality is a value that makes the inequality true Solving addition and subtraction equations Solving multiplication and division equations Understanding inequalities Understand equality Solve addition, subtraction, multiplication and division equations Understand inequalities Work backward to solve a problem Unit 18 Pretest 18

19 or Understandings Unit 19 Transformations, Congruence, and Symmetry Shapes in the plane can be translated to another position in the plane. The translated image is the same size and shape as the original figure Shapes in the plane can be reflected across a line. The reflected image is the same size and shape as the original figure Shapes in the plane can be rotated around a point. The rotated image is the same size and shape as the original figure Congruent figures remain congruent Translations Reflections Rotations Congruent figures Line symmetry Rational symmetry Identify the translation, reflection and rotation of a figure Identify which motion can be used to show if two figures are congruent Identify line and rotational symmetry in figures Unit 19 Pretest 19

20 Unit 20 Probability Counting techniques exist for finding the number of possible combinations The outcomes of an event can be represented pictorially using a tree diagram and counted to find the number of possible outcomes The chance or likelihood of an event occurring, called its probability, can be expressed as a number between 0 and 1 inclusive Finding combinations Outcomes and tree diagrams Writing probability as a fraction Find combinations and outcomes Describe the likelihood of an event Find probability as a fraction Unit 20 Pretest 20