Fourth Grade- Unit 1- Whole Numbers, Place Value, and Rounding Computation Unit – 1 - Whole Numbers, Place Value and Rounding in Computation MCC4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. MCC4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. MCC4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Essential Questions How do digit values change as they are moved around in large numbers? What determines the value of a digit? How does estimation keep us from having to count large numbers individually? How are large numbers estimated? What conclusions can I make about the places within our base ten number system? What happens to a digit when multiplied and divided by 10? What effect does the location of a digit have on the value of the digit? How do digit values change as they are moved around in large numbers? What determines the value of a digit? How can we compare large numbers? What determines the value of a number? Why is it important for me to be able to compare numbers? What is a sensible answer to a real problem? What information is needed in order to round whole number to any place? How can I ensure my answer is reasonable? How can rounding help me compute numbers? Tasks/ On-Core Building 1,000- Task 1 Lesson 15 Lesson 16 Relative Value of Places- Task 2 Lesson 15 Lesson 17 Lesson 31 Number Scramble- Task 3 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Ticket Master- Task 4 Lesson 15 Lesson 18 Nice Numbers- Task 5 Lesson 19 Weeks/ Days 1 Day 2 Days 1 Day 1 Day 1 Day
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Fourth Grade- Unit 1- Whole Numbers, Place Value, and Rounding Computation
Unit – 1 - Whole Numbers, Place Value and Rounding in Computation
MCC4.OA.1 Interpret a
multiplication equation as a
comparison, e.g., interpret 35 = 5 × 7
as a statement that 35 is 5 times as
many as 7 and 7 times as many as
5. Represent verbal statements of
multiplicative comparisons as
multiplication equations.
MCC4.OA.2 Multiply or divide to
solve word problems involving
multiplicative comparison, e.g., by
using drawings and equations with a
symbol for the unknown number to
represent the problem, distinguishing
multiplicative comparison from
additive comparison.
MCC4.OA.3 Solve multistep word
problems posed with whole numbers
and having whole-number answers
using the four operations, including
problems in which remainders must
be interpreted. Represent these
problems using equations with a
letter standing for the unknown
quantity. Assess the reasonableness
of answers using mental computation
and estimation strategies including
rounding.
Essential Questions
How do digit values change as they are moved around in large numbers?
What determines the value of a digit?
How does estimation keep us from having to count large numbers individually?
How are large numbers estimated?
What conclusions can I make about the places within our base ten number system?
What happens to a digit when multiplied and divided by 10?
What effect does the location of a digit have on the value of the digit?
How do digit values change as they are moved around in large numbers?
What determines the value of a digit?
How can we compare large numbers?
What determines the value of a number?
Why is it important for me to be able to compare numbers?
What is a sensible answer to a real problem?
What information is needed in order to round whole number to any place?
How can I ensure my answer is reasonable?
How can rounding help me compute numbers?
Tasks/ On-Core Building 1,000- Task 1 Lesson 15 Lesson 16
Center Three 1 Day (Refer back to Task 10 in Unit 2) (This lesson references Algebraic Expressions) 1 Day
Teacher notes: Vocabulary:
common fraction composite denominator equivalent sets factor improper fraction increment mixed number numerator prime proper fraction term unit fraction whole number
Fourth Grade- Unit 3- Adding and Subtracting Fractions
Unit – 3- Adding and Subtracting Fractions
MCC4.NF.3 Understand a fraction
a/b with a > 1 as a sum of fractions
1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the
Essential Questions
What happens to the denominator when I add fractions with like denominators?
Why does the denominator remain the same when I add fractions with like denominators?
How do we add fractions with like denominators?
What is a fraction and how can it be represented?
How can equivalent fractions be identified?
How can fraction represent parts of a set?
How can I add and subtract fractions of a given set?
1 Day 1 Day/ Center One (Summative Assessment) Center Two 1 Day
What is an improper fraction and how can it be represented?
What is a mixed number and how can it be represented?
What is the relationship between a mixed number and an improper fraction?
How can improper fractions and mixed numbers be used interchangeably?
How do we add fractions?
How do we apply our understanding of fractions in everyday life?
(Students select two Pizzas: one with improper fractions and one with common fractions.)
Teacher notes: Vocabulary: Fraction denominator equivalent sets improper fraction increment mixed number numerator proper fraction term unit fraction whole number
Fourth Grade- Unit 4- Multiplying and Dividing Fractions
Unit – 4- Multiplying and Dividing Fractions
MCC4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Essential Questions
How can I be sure fractional parts are
equal in size?
What do the numbers (terms) in a fraction represent?
How does the number of equal pieces affect the fraction name? • How can I write a fraction to represent a part of a group?
How can I represent a fraction of a discrete model (a set)?
How are multiplication, division, and fractions related?
What does it mean to take a fraction portion of a whole number?
How is multiplication of fractions similar to division of whole numbers?
How do we determine the whole amount when given a fractional value of the whole?
How do we determine a fractional value when given the whole number?
How can fraction represent parts of a set?
How can I represent fractions in different ways?
How can I find equivalent fractions?
How can I multiply a set by a fraction?
What strategies can be used for finding
Tasks/ On-Core A Bowl of Beans- Task 1 Birthday Cake!- Task 2 Fraction Clues- Task 3 Area Models- Task 4
Weeks/ Days/ Centers
products when multiplying a whole number by a fraction?
How can I model the multiplication of a whole number by a fraction?
What does it mean to take a fractional portion of a whole number?
How is multiplication of fractions similar to division of whole numbers?
How is multiplication of fractions similar to repeated addition of fraction?
What is the relationship between the size of the denominator and the size of each fractional piece (i.e. the numerator)?
How can we use fractions to help us solve problems?
How can we model answers to fraction problems?
How can we write equations to represent our answers when solving word problems?
How can I multiply a whole number by a fraction?
What is the relationship between multiplication by a fraction and division?
How can I represent multiplication of a whole number?
What does it mean to take a fraction portion of a whole number?
How is multiplication of fractions similar to division of whole numbers?
How do we determine the whole amount when given a fractional value of the whole?
Fraction Pie Game- Task 5 Birthday Cookout- Task 6 Fraction Farm- Task 7 Land Grant (Culminating)- Task 8
How do we determine a fractional value when given the whole number?
Teacher notes: Vocabulary
Fraction denominator equivalent sets improper fraction Increment mixed number numerator proper fraction Term unit fraction whole number
Fourth Grade- Unit 5- Fractions and Decimals Unit – 5- Fractions and Decimals
4.NF Understand decimal notation for fractions and compare decimal fractions. MCC4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/1001. MCC4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. MCC4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of the comparisons with the symbols >, =, or <, and justify the conclusions, e.g. by using a visual model.
Essential Questions
What are the characteristics of a decimal
fraction?
What patterns occur on a number line made up of decimal fractions?
What role does the decimal point play in our base-ten system?
How can I model decimal fractions using the base-ten and place value system?
How are decimal fractions written using decimal notation?
What is a decimal fraction and how can it be represented?
What is a decimal fraction and how can it be represented?
When is it appropriate to use decimal fractions?
How are decimal numbers and decimal fractions related?
How can decimals and decimal fractions be represented as a part of a whole?
When can tenths and hundredths be used interchangeably?
When you compare two decimals, how can you determine which one has the greater value?
Tasks Decimal Fraction Number Line- Task 1 Base Ten Decimals- Task 2 Decimal Designs- Task 3 Flag Fractions- Task 4 Dismissal Duty Dilemma- Task 5 Expanding Decimals with Money- Task 6
Weeks/ Days
When can tenths and hundredths be used interchangeably?
When you compare two decimals, how can you determine which one has the greater value?
How are decimals and fractions related?
Why is the number 10 important in our number system?
How can I write a decimal to represent a part of a group?
When we compare two decimals, how do we know which has a greater value?
When adding decimals, how does decimal notation show what I expect? How is it different?
What models can be used to represent decimals?
What are the benefits and drawbacks of each of these models?
How does the metric system of measurement show decimals?
How can I combine the decimal length of objects I measure?
What models can be used to represent decimals?
What are the benefits and drawbacks of each of these models?
Double Number Line Decimals- Task 7 Trash Can Basketball- Task 8 Calculator Decimal Counting- Task 9 Meter of Beads- Task 10 Measuring Up- Task 11 Decimal Line Up- Task 12
How do you order two-digit decimal fractions?
How are decimal numbers and decimal fractions related?
What is a decimal fraction and how can it be represented?
When is it appropriate to use decimal fractions?
How can decimal fractions help me determine the best choices on how to spend my money?
How can I determine the best cell phone plan?
In the Paper- Task 13 Taxi Trouble- Task 14 Cell Phone Plans (Culminating)- Task 15
Teacher notes: Vocabulary
Decimal decimal fraction decimal point denominator equivalent sets increment numerator term unit fraction whole number
Fourth Grade- Unit 6- Geometry
Unit – 6- Geometry 4.G Draw and identify lines and angles, and classify shapes by properties of their lines and angles. MCC. 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. MCC.4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. MCC.4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
Essential Questions
What are the geometric objects that make up figures?
What are the mathematical conventions and symbols for the geometric objects that make up certain figures?
How can we sort two-dimensional figures by their angles?
What makes an angle a right angle?
How can you use only a right angle to classify all angles?
What properties do geometric objects have in common?
How are geometric objects different from one another?
What are triangles?
How can you create different types of triangles?
How are triangles alike and different?
What are the properties of triangles?
How can triangles be classified by the measure of their angles?
How can angle and side measures help us to create and classify triangles?
Tasks What Makes a Shape?- Task 1 Angle Shape Sort- Task 2 Is This the Right Angle?- Task 3 Be an Expert- Task 4 Thoughts About Triangles- Task 5 My Many Triangles- Task 6
Weeks/ Days
What is a quadrilateral?
How can you create different types of quadrilaterals?
How are quadrilaterals alike and different?
What are the properties of quadrilaterals?
How can the types of sides be used to classify quadrilaterals?
What is symmetry?
How are symmetrical figures created?
How do you determine lines of symmetry? What do they tell us?
How is symmetry used in areas such as architecture and art? In what areas is symmetry important?
How do you determine lines of symmetry? What do they tell us?
How are symmetrical figures used in artwork?
Which letters of the alphabet are symmetrical?
Where is geometry found in your everyday world?
How can shapes be classified by their angles and lines?
How can you determine the lines of symmetry in a figure?
Quadrilateral Roundup- Task 7 Superhero Symmetry- Task 8 Line Symmetry- Task 9 A Quilt of Symmetry- Task 10 Decoding ABC Symmetry- Task 11 Geometry Town (Culminating)- Task 12
Teacher notes: Vocabulary: acute angle angle equilateral triangle isosceles triangle line of symmetry obtuse angle parallel lines parallelogram perpendicular lines plane figure polygon quadrilateral rectangle rhombus right angle scalene triangle side square symmetry triangle trapezoid vertex (of a 2-D figure)
Fourth Grade- Unit 7- Measurement Unit – 7- Measurement MCC4.MD.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36) MCC4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. MCC4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a
Essential Questions
What is a unit?
How are the units of linear measurement within a standard system related?
Why are units important in measurement?
How are data collected?
How do we determine the most appropriate graph to use to display the data?
How will we interpret a set of data?
How do graphs help explain real-world situations?
How is perimeter different from area?
What is the relationship between area and perimeter when the area is fixed?
What is the relationship between area and perimeter when the perimeter is fixed?
How does the area change as the rectangle’s dimensions change (with a fixed perimeter)?
How are the units used to measure perimeter like the units used to measure area?
How are the units used to measure perimeter different from the units used to measure area?
What is the difference between a gram and a kilogram?
What is weight (mass when using a
Tasks Measuring Mania- Task 1 What’s the Story?- Task 2 Perimeter and Area- Task 3 Setting the Standard- Task 4
Weeks/ Days
multiplication equation with an unknown factor. Represent and interpret data. MCC4.MD.4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. A line plot shows the “shape” of the data and provides the foundation for future data concepts, such as mode and range. Geometric Measurement - understand concepts of angle and measure angles. MCC4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n
balance)?
Why do we measure weight?
What units are appropriate to measure weight?
What around us weighs about a gram?
How are units in the same system of measurement related?
What happens to a measurement when we change units?
How are grams and kilograms related?
What around us weighs about a gram? About a kilogram?
When should we measure with grams? Kilograms?
What happens to a measurement when we change units?
Why are units important in measurement?
What units are appropriate to measure weight?
How heavy does one pound feel?
What do you do if a unit is too heavy to measure an item?
What units are appropriate to measure weight?
When do we use conversion of units?
Why are units important in measurement?
What happens to a measurement when we change units?
Worth the Weight- Task 5 A Pound of What?- Task 6 Exploring an Ounce- Task 7 Too Heavy? Too Light?- Task 8
degrees. MCC4.MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. MCC4.MD.7. Recognize angle measure as additive. When an angle is decomposed into non- overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Can different size containers have the same capacity?
How can we estimate and measure capacity?
How are fluid ounces, cups, pints, quarts, and gallons related?
How can fluid ounces, cups, pints, quarts, and gallons be used to measure capacity?
Why do we need to be able to convert between capacity units of measurement?
How do we compare metric measures of milliliters and liters?
How do we compare customary measures of fluid ounces, cups, pints, quarts, and gallons?
What happens to a measurement when we change units?
How do we use weight measurement?
Why is it important to be able to measure weight?
How do we compute area and perimeter?
Why are standard units important?
How does a circle help with measurement?
How are a circle and an angle related?
How is a circle like a ruler?
Capacity Line-Up- Task 9 More Punch Please!- Task 10 Water Balloon Fun!- Task 11 Dinner at the Zoo/ Naptime at the Zoo (Culminating)- Task 12 Which Wedge is Right?- Task 1 Angle Tangle- Task 2 Build an Angle Ruler- Task 3
How can we measure angles using wedges of a circle?
How do we measure an angle using a protractor?
Why do we need a standard unit with which to measure angles?
What are benchmark angles and how can they be useful in estimating angle measures?
How does a turn relate to an angle?
What does half rotation and full rotation mean?
What do we actually measure when we measure an angle?
How are the angles of a triangle related?
What do we know about the measurement of angles in a triangle?
How can we use the relationship of angle measures of a triangle to solve problems?
How can angles be combined to create other angles?
How can we use angle measures to draw reflex angles?
Guess My Angle!- Task 4 Turn, Turn, Turn- Task 5 Summing It Up- Task 6 Angles of Set Squares (Culminating)- Task 7
Teacher notes: Vocabulary centimeter(cm) cup (c) customary foot (ft) gallon (gal) gram (g) kilogram (kg) kilometer (km) liquid volume liter (L) mass measure meter (m) metric mile (mi) milliliter (mL) ounce (oz) pint (pt) pound (lb) quart (qt) relative size ton weight yard (yd) data line plot acute angle angle arc circle degree measure obtuse angle one-degree angle protractor reflex angle right angle straight angle intersect