grade 3 math pacing guide -...

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Grade 3 Math Pacing Guide

This pacing guide is designed so concepts connect to prior learning and build throughout the year while ensuring all standards are taught prior to the state testing window. A suggested sequence is provided to ensure a logical progression of concepts. Use professional judgment to adjust the amount of time spent on concepts based on the needs of your students. Major concepts are broken into smaller chunks so that struggling students have time to work on mastering a small piece before moving on to the more difficult aspects of a concept. This also makes spiraling and keeping standards at the forefront of student thinking much more manageable.

*This will be taught twice a week using contextual problems and during daily class work. (You will teach strategies during the twice weekly contextual problem time)

** Graphs will be used throughout the year across the curriculum, so students will have a great deal of exposure to graphs before this time.

O: On-going standards are continually instructed and assessed throughout the year E: Standard explicitly instructed standards are introduced and taught with explicit, direct instruction. M: Standard instructed and assessed indicates mastery, though re-teaching and assessment are expected through the end of the school year. Highlighted standards Highlighted standards are identified as Power-Standards, based on the TN Ready blueprints.

Operations and Algebraic Thinking Number and Operations in Base Ten

Q1 Q2 Q3 Q4 Standard Q1 Q2 Q3 Q4 Standard

E O M 3.OA.A.1 10-14 Items 22-29% of test E M 3.NBT.A.1 10-14 Items 22-29% of test

E/O M 3.OA.A.2 10-14 Items 22-29% of test E M 3.NBT.A.2 10-14 Items 22-29% of test

E O M 3.OA.A.3 10-14 Items 22-29% of test E/M 3.NBT.A.3 10-14 Items 22-29% of test

E O E M 3.OA.A.4 10-14 Items 22-29% of test Number and Operations- Fractions

E O E M 3.OA.B.5 7-10 Items 9-15% of test E O M 3.NF.A.1 4-6 Items 9-15% of test

E/O M 3.OA.B.6 7-10 Items 9-15% of test E O M 3.NF.A.2 4-6 Items 9-15% of test

E/O O O M 3.OA.C.7 10-14 Items 22-29% of test E O M 3.NF.A.2a 4-6 Items 9-15% of test

E O O O *3.OA.D.8 7-10 Items 9-15% of test E O M 3.NF.A.2b 4-6 Items 9-15% of test

E O M 3.OA.D.9 7-10 Items 9-15% of test E O M 3.NF.A.3 4-6 Items 9-15% of test

Measurement and Data E O M 3.NF.A.3a 4-6 Items 9-15% of test

Q1 Q2 Q3 Q4 Standard E O M 3.NF.A.3b 4-6 Items 9-15% of test

E/O M 3.MD.A.1 13-20 Items 33-40% of test E O M 3.NF.A.3c 4-6 Items 9-15% of test

E M 3.MD.A.2 13-20 Items 33-40% of test E O M 3.NF.A.3d 4-6 Items 9-15% of test

**E/M 3.MD.B.3 13-20 Items 33-40% of test

E/O M 3.MD.B.4 13-20 Items 33-40% of test Geometry

E/M 3.MD.C.5 13-20 Items 33-40% of test Q1 Q2 Q3 Q4 Standard

E/M 3.MD.C.5a 13-20 Items 33-40% of test E/M 3.G.A.1 13-20 Items 33-40% of test

E/M 3.MD.C.5b 13-20 Items 33-40% of test E/M 3.G.A.2 13-20 Items 33-40% of test

E/M 3.MD.C.6 13-20 Items 33-40% of test E M 3.G.A.3 13-20 Items 33-40% of test

E 3.MD.C.7 13-20 Items 33-40% of test

E/M 3.MD.C.7a 13-20 Items 33-40% of test

E/M 3.MD.C.7b 13-20 Items 33-40% of test

E M 3.MD.C.7c 13-20 Items 33-40% of test

E M 3.MD.C.7d 13-20 Items 33-40% of test

E O M 3.MD.D.8 13-20 Items 33-40% of test

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2018-2019 School Year

1st Quarter: Aug. 6th – Sept. 28th 40 days Wk 1: 3.NBT.A.2 Place value, addition, and subtraction

Wk 2: 3.NBT.A.2 Place value, addition, and subtraction

*while we will not be discussing arrays until the 5th week the students do have background knowledge of arrays, so you can begin to have them work on memorization of 0s, 1s. 2s, 5s, and 10s

Wk 3: 3.OA.C.7 Multiplying and Dividing within 100

*while we will not be discussing arrays until the 5th week the students do have background knowledge of arrays, so you can begin to have them work on memorization of 0s, 1s. 2s, 5s, and 10s (Students will work on multiplication and division memorization for the entire year according to how your school accomplishes this task)

3.NBT.A.1 Rounding and estimating to solve addition and subtraction problems

Wk 4: 3.NBT.A.1 Rounding and estimating to solve addition and subtraction problems

Wk 5: 3.OA.A.1, 3.OA.B.5, and 3.OA.D.9 Arrays, properties of multiplication (zero, identity, associative and commutative), and Identify arithmetic patterns and explain them using operations *3 day week

Wk 6: 3.OA.A.1, 3.OA.B.5, and 3.OA.D.9 Arrays, properties of multiplication (zero, identity, associative and commutative), and Identify arithmetic patterns and explain them using operations

Wk 7: 3.OA.A.4 Determine the unknown whole number in multiplication or division equations (Multiplication and Division Fact Families)

Wk 8: 3.GA.2 and 3.NF.A.1 Fractions as equal parts (partitioning) and naming fractions

2nd Quarter: Oct. 8th- Dec. 19th 48 days

Wk 1: 3.MD.D.8 Finding perimeter using real-world situations and unknowns

Wk 2: 3.MD.C.5 and 3.MD.C.6 Area (counting squares)

Wk 3: 3.NF.A.2 a-b Fractions on a Number line

Wk 4: 3.NF.A.3 a-d Comparing and Equivalent Fractions

Wk 5: 3.NF.A.3 a-d Comparing and Equivalent Fractions

Wk 6: 3.MD.A.1 Telling time to the nearest minute *4-day week

Wk 7: 3.MD.B.4 Measuring to the nearest ½ inch and line plots

Wk 8: 3.OA.A.3 Finding unknowns in multiplication and division problems using what you know about the relationship between the two

Wk 9: 3.MD.A.1 Elapsed time using contextual problems

Wk 10: 3.OA.B.5 Properties of multiplication (review and add distributive) and 3.NBT.A.3 Multiplying one-digit whole numbers by multiples of 10 *3 day week

3rd Quarter: Jan. 8th-Mar. 8th 42 days

Wk 1: 3.OA.A.2 and 3.OA.B.6 Division *4 day week

Wk 2: 3. MD.C.7a-b Relating area to multiplication and addition

Wk 3: 3.MD.A.2 Metric Measurement Mass and Volume *4-day week

Wk 4: 3.MD.A.2 Metric Measurement Mass and Volume

Wk 5: 3.MD.B.4 Measure to the nearest ¼ inch and line plots

Wk 6: 3.MD.C.7 c-d Area using the distributive property and finding area of irregular rectilinear shapes

Wk 7: 3.MD.C.7c-d Area using the distributive property and finding area of irregular rectilinear shapes *4 day week

Wk 8: 3.G.A.3 and 3.G.A.1 Polygons and Quadrilaterals

Wk 9: 3.G.A.3 and 3.G.A.1 Polygons and Quadrilaterals

4th Quarter: Mar. 12th – May 21st 45 days

Wk 1: 3.MD.B.3 Bar Graph and Pictograph *4-day week

Wk 2: 3.MD.B.3 Bar Graph and Pictograph

Wk 3: Review and TN Ready

Wk 4: Review and TN Ready Practice

Wk 5: Review and TN Ready Practice

Wk 6:

Wk 7:

Wk 8:

Wk 9: 2 Days

3

Grade 3 Math Pacing Guide Quarter 1

Quarter 1 Number Talks and Contextual Problems

Suggested Number Talks (Mondays and Wednesdays):

Addition Strategy: Making Landmark or Friendly Numbers

Addition Strategy: Breaking Numbers into Parts

Addition Strategy: Adding Up in Chunks

Suggested Contextual Problem Topics (Tuesdays and Thursdays)

3.OA.D.8 Addition, Subtraction, Estimating

Week 1 and 2

Adding and Subtracting Rationale for Sequence Prior Knowledge

• Make connections between various strategies (i.e. base-ten, number lines, partial sums, expanded form addition or subtraction, and traditional algorithm)

• Fluently add and subtract within 1,000 using a range of algorithms

Addition and Subtraction were two major skills in 2nd grade. We started here to allow the students to start the year off on familiar territory while allowing them to adjust to the pace and expectations of 3rd grade.

In second grade, students added and subtracted within 1,000 using concrete models or drawings and strategies based on place value, properties of operations, and the relationship between addition and subtraction. Students have worked toward mastery of all problem types by the end of second grade. (See Tennessee Math Standards Table 1 Common addition and subtraction situations)

Standards Resources I Can Statements

3.NBT.A.2 (SUPPORTING) Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Academic Vocabulary: addends, sum, subtrahend, difference

https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-add-sub-topic/cc-3rd-adding-carrying/v/carrying-when-adding-three-digit-numbers

http://www.softschools.com/math/addition/3_digit_addition/3_digit_addition_with_regrouping/

https://www.youtube.com/watch?v=nku3jVLbPBw

https://www.pinterest.com/pin/120330621263591365/

https://www.khanacademy.org/math/arithmetic/arith-review-add-subtract/arith-review-regrouping-3-dig/v/regrouping-twice-when-subtracting-three-digit-numbers

http://www.teachertube.com/video/subtracting-across-zeros-271905

I can fluently add and subtract within 1,000 using an algorithm and strategy based on place value.

I can use strategies (such as applying the commutative or associative property, adding on, using an open number line, drawing models, compensation, etc.) for adding and subtracting within 1,000 with ease.





https://www.youtube.com/watch?v=nku3jVLbPBw





http://www.teachertube.com/video/subtracting-across-zeros-271905

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Weeks 3 and 4

Rounding Rationale for Sequence Prior Knowledge

• Understand rounding is useful for estimating and determining the reasonableness of a solution

• Round 2- and 3-digit numbers to the nearest ten and hundred

• Explain reasoning using number lines, midpoints, a hundred chart, and a place value chart

Rounding comes after addition and subtraction to help students assess the reasonableness of their answers when solving contextual problems.

In second grade, students relied on place value understanding to compare 3-digit numbers using concrete models such as base-ten blocks, place value charts, and number lines. Students used symbols <, >, and = to compare numbers.


3.NBT.A.1 (SUPPORTING) Round whole numbers to the nearest 10 or 100 using understanding of place value.

3.OA.C.7 (MAJOR)Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of 3 rd grade, know from memory all products of two one-digit numbers and related division facts.

Academic Vocabulary: estimate, rounding

https://www.illustrativemathematics.org/content-standards/3/NBT/A/1

http://www.abcya.com/rounding_numbers.htm

I can use place value to round whole numbers to the nearest 10 and 100.

I can multiply and divide within 100. (this will be an I can statement for the rest of the year)



http://www.abcya.com/rounding_numbers.htm

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Week 5 and 6

Multiplication Rationale for Sequence Prior Knowledge

• Understand the terminology and meaning in a multiplication equation

• Begin to apply properties related to multiplication (zero, identity, associative and commutative)

At this point, students need to begin to understand multiplication on a deeper level, in order to become fluent with their multiplication facts.

In second grade students gained a knowledge of arrays and what they mean.


3.OA.A.1(MAJOR) Interpret the factors and products in whole number multiplication equations (e.g., 4 x7 is 4 groups of 7 objects with a total of 28 objects or 4 strings measuring 7 inches each with a total of 28 inches

3.OA.B.5 (MAJOR) Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (Associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (Distributive property of multiplication over addition).

3.OA.D.9 (MAJOR) Identify arithmetic patterns (including patterns in addition and multiplication tables) and explain them using properties of operations. For example, analyze patterns in the multiplication table and observe that 4 times a number is always even (because 4 x 6 = (2 x 2) x 6, which uses the associative property of multiplication) (See Table 3- Properties of Operations)

Academic Vocabulary: multiplication, factor, product, commutative property, associative property

https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/e/commutative-property-of-multiplication

https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/e/associative-property-of-multiplication-

(3.OA.A.1) I can illustrate products of whole numbers in relations to factors (e.g., 35=5 x 7 can be interpreted as 5 groups of 7, an array with 5 rows and 7 columns, the area of a 5-by-7 rectangle, 5 rows of 7 objects).

(3.OA.A.1)I can multiply to find the product of two single digit whole numbers.

(3.OA.A.1)I can recognize multiplication as repeated addition.

(3.OA.A.1)I can use skip counting as a strategy to find a product of two factors.

(3.OA.B.5) I can distinguish between the properties of multiplication.

(3.OA.B.5)I can apply the properties of multiplication to solve problems more efficiently.

(3.OA.B.5)I can justify my thinking using algebraic properties as proof.

(3.OA.B.5)I can explain the commutative and associative property of multiplication.

(3.OA.B.5)I can apply the commutative, associative, properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.

(3.OA.D.9) I can recognize and describe arithmetic patterns in number charts, charts, addition tables, and multiplication tables.

(3.OA.D.9) I can analyze arithmetic patterns using properties of operations.

(3.OA.D.9) I can explain why an even number times any number is always even. (For example, I can explain why 4 times a number is always even and why 4 can be decomposed into two equal addends.)









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Week 7

Multiplication and Division Rationale for Sequence Prior Knowledge

• Understand the inverse relationship between multiplication and division

Now that students have a working knowledge of multiplication, they need to understand that division is the inverse operations of multiplication.

Standards Resources I Can Statement

3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers within 100. For example, determine the unknown number that makes the equation true in each of the equations: 8 x ? =48, 5 = ? ÷3, 6 x 6 = ?

Academic Vocabulary: division, dividend, divisor, quotient

I can solve problems by finding the missing factor, product, divisor, dividend, or quotient.

I can generate the unknown number, no matter its position, in multiplication and division problems.

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Week 8

Fraction Meanings Rationale for Sequence Prior Knowledge

• Understand that fractions are equal parts of a whole(s)

• Explain a numerator and denominator

• Name a fraction

An understanding of whole numbers provides a foundation for students to make sense of fractions. Multiplication concepts of equal groups and equal shares helps students make sense of partitioning regions, shapes, and number lines.

In prior grades, students have divided shapes into equal parts and have named the parts as halves, thirds, and fourths (students have not used fraction notation).


3.G.A.2 (SUPPORTING) Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area and describe the area of each part as 1/4 of the area of the shape.

3.NF.A.1 (MAJOR) Understand a fraction, 1/b, as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction a/b as the quantity formed by a parts of size 1/b. For example, ¾ represents a quantity formed by 3 parts of size ¼.

Academic Vocabulary: equal parts, unit fraction, fraction, denominator, numerator

https://video.search.yahoo.com/yhs/search?fr=yhs-itm-001&hsimp=yhs-001&hspart=itm&p=fraction+video+for+kids#id=1&vid=9a75a2f82b1da3850e86e1f607fa9f21&action=click

https://indulgy.com/post/NiIffm97f1/fractions-anchor-chart

http://realteacherslearn.blogspot.com/2013/05/math-manipulatives-and-fraction-art.html (only the fraction part)

http://www.harcourtschool.com/activity/cross_the_river/

(3.G.A.2) I can partition (divide) shapes into equal parts with equal areas.

(3.G.A.2) I can explain any unit fraction (1/b) as one part of a whole divided into b equal parts (e.g., ½, ¼, 1/8,) (Relate 1/8 on a ruler.)

(3.NF.A.1) I can explain any unit fraction (1/b) as 1 part of a whole.

(3.NF.A.1) I can explain any fraction a/b as "a" (numerator) representing the number of parts and "b" (denominator) representing the total number of equal parts in the whole; for example, ¾ represents a quantity formed by 3 parts of size ¼.







http://realteacherslearn.blogspot.com/2013/05/math-manipulatives-and-fraction-art.html

http://realteacherslearn.blogspot.com/2013/05/math-manipulatives-and-fraction-art.html

http://www.harcourtschool.com/activity/cross_the_river/

8




Subtraction Strategy: Adding Up to Find the Difference

Subtraction Strategy: Expanded Form

Subtraction Strategy: Base 10

Suggested Contextual Problem Topics (Tuesdays and Thursdays)

3.OA.D.9 Addition, Subtraction, Multiplication and Perimeter

Week 1

Perimeter Rationale for Sequence Prior Knowledge

• Solve real world problems of polygons to find the perimeter or the unknown side length

Perimeter is here because students have a good understanding of adding. By placing it here, it separates it from area so that when we get to area next week the students realize they are two different ideas and will not interchange them as much.

In second grade, students added together length measurements to find a total measurement around an object.


3.MD.D.8 (SUPPORTING) Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Academic Vocabulary: polygon, perimeter, unknown side length

https://www.pinterest.com/pin/Aeu-E27sBCAxsChQBKcnzu5ivBV0ZcVxIjrHHKIq8NmsDWPYfHBstUE/

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/basic-geo-perimeter/v/finding-missing-a-side-length-when-given-perimeter-math-3rd-grade-khan-academy

https://video.search.yahoo.com/yhs/search?fr=yhs-itm-001&hsimp=yhs-001&hspart=itm&p=perimeter+video+for+kids#id=13&vid=b2884b2a988cc98db601b025a61cfcbc&action=view

https://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/PerimeterShapesShoot.htm

I can calculate the perimeter of shapes made from polygons.

I can calculate the perimeter of a polygon with a missing side.

I can construct shapes with different areas given the same perimeter.

I can construct shapes with different perimeters given the same area.












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Week 2

Area Rationale for Sequence Prior Knowledge

• Use tiling and counting to measure rectangles

Area, is introduced here so that students can see quickly how it is different from perimeter. Since most students will still be working to master their multiplication facts we are only dealing with area as it relates to counting square units.

Students have knowledge of linear measurement from primary grades and have learned rules of measurement. In second grade, they used same-sized squares to tile a rectangle and decompose a rectangle into rows and columns.


3.MD.C.5 (MAJOR) Recognize that plane figures have an area and understand concepts of area measurement.

a. Understand that a square with side length 1 unit, called "a unit square," is said to have "one square unit" of area and can be used to measure area.

b. Understand that a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

3.MD.C.6 (MAJOR) Measure areas by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units).

Academic Vocabulary: unit squares, area, plane figure

https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/basic-geo-unit-squares-area/v/introduction-to-area-and-unit-squares


https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/basic-geo-unit-squares-area/e/area_1

https://www.youtube.com/watch?v=Tpy09HOkHyI

(3.MD.C.5) I can describe plane figures by their attributes such as length, width, and area.

(3.MD.C.5)I can interpret the space inside a plane figure as its area.

(3.MD.C.5)I can define a unit square.

(3.MD.C.5)I can describe area as the measure of space within a plane figure and explain why area is measured in square units.

(3.MD.C.5)I can explain that multiplying a length by a width (which are single dimensions) results in an area measure (2 dimensions).

(3.MD.C.5) I can determine the measure of the area of a plane figure by covering the space inside it with color tiles and counting them.

(3.MD.C.6) I can represent the area of a plane figure as "n" square units (not units squared).







https://www.youtube.com/watch?v=Tpy09HOkHyI

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Week 3


• Understand that fractions have different meanings: fractions of a region and fractions of a number line

An understanding of whole numbers provides a foundation for students to make sense of fractions. Multiplication and division concepts of equal groups and equal shares helps students make sense of partitioning regions, shapes, and number lines.



3.NF.A.2 (MAJOR)Understand a fraction as a number on the number line. Represent fractions on a number line.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint locates the number 1/b on the number line. For example, on a number line from 0 to 1, students can partition it into 4 equal parts and recognize that each part represents a length of ¼ and the first part has an endpoint at ¼ on the number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. For example, 5/3 is the distance from 0 when there are 5 iterations of 1/3.

Academic Vocabulary: fraction number line, interval, partitioning, endpoint

https://docs.google.com/file/d/0B_wlnPzXZBUZMjEyMWQxMjAtMzRiNy00ZjYxLWJkMjYtZGU5NjYzYTIwOTUw/edit?pli=1

I can explain and show how 1/b can be represented on a number line as a number that is located a distance of 1/b to the right of 0.

I can explain and show 1/b can be represented on a number line as the size of each part when a whole is partitioned into b equal groups. For example on a number line from 0 to 1, students can partition it into 4 equal parts and recognize that each part represents a length of ½ and the first part has an endpoint at ¼ on the number line.

I can represent a unit fraction 1/b on a number line between 0 and 1 by creating a number line with the appropriate number of tick marks and spaces between whole numbers. For example, 5/3 is the quantity you get when combining 5 parts together when the whole is divided into 3 equal parts.




11

Weeks 4-5


• Explain fractional equivalence to whole numbers

• Compare unit fractions by reasoning about their size

An understanding of whole numbers provides a foundation for students to make sense of fractions. Multiplication and division concepts of equal groups and equal shares helps students make sense of partitioning regions, shapes, and number lines.



3.NF.A.3 (MAJOR) Explain equivalence of fractions and compare fractions by reasoning about their size.

a. Understand two fractions are equivalent (equal) if they are the same size or at the same point on a number line.

b. Recognize and generate simple equivalent fractions and explain why the fractions are equivalent using a visual fraction model.

c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions.

Academic Vocabulary: equivalence, <,>, = as related to fractions

https://www.k-5mathteachingresources.com/support-files/roll-a-fraction.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/3-5/FractionsLength-AS-ComparingOrdering.pdf

https://www.visualfractions.com/worksheets/compare/compareworksheets.pdf

https://learnzillion.com/lesson_plans/8991-compare-fractions-with-the-same-denominator-by-reasoning-about-their-size/

https://www.mathgames.com/skill/3.43-compare-fractions

https://learnzillion.com/lesson_plans/8304-express-whole-numbers-as-fractions/

I can use models to show and explain the equivalent fractions with denominators of 2,3,4,6, and 8.

I can locate equivalent fractions on a number line.

I can determine that two fractions are equivalent when they are the same size or at the same point on a number line.

I can use different visual fraction models to justify that one fraction is equivalent to another.

I can create equivalent fractions and represent them with pictures and models.

I can use models to show and explain whole numbers as fractions.

I can locate whole numbers as fractions on a number line.

I can use models to compare two fractions and record the comparison using >,<, or =.

I can explain how the size of equal parts can be used to compare two fractions with the same numerator.

I can divide a whole into different fractional parts and compare.

I can use visual models to name fractions as less than, equal to, or greater than one.

I can sort fractions as less than, equal to, or greater than one-half.











https://www.mathgames.com/skill/3.43-compare-fractions



12

Week 6

Time Rationale for Sequence Prior Knowledge

• Tell and write time to the nearest minute

By separating time to the nearest minute from elapsed time, we are allowing for teachers to work in small groups with students who struggle with telling time to the nearest minute before moving on to elapsed time.

In previous grades, students learned to tell time to the hour, half hour, quarter hour, and five minutes. In second grade, students notate a.m. and p.m. when recording time.

Standards

Resources I Can Statements

3.MD.A.1 (MAJOR) Tell and write time to the nearest minute and measure time intervals in minutes.

Academic Vocabulary: hour hand, minute hand, interval of time

https://learnzillion.com/lesson_plans/5772-reading-the-exact-time-on-a-clock/#lesson

http://mrnussbaum.com/bedtime-2/

https://video.search.yahoo.com/yhs/search?fr=yhs-itm-001&hsimp=yhs-001&hspart=itm&p=time+am+and+pm+video#id=4&vid=bf7d6b4918b17ceecdf5118813dadef1&action=click

https://gb.education.com/game/am-and-pm-quiz/

I can say and write time to the nearest minute.

I can measure duration of time in minutes.



http://mrnussbaum.com/bedtime-2/





https://gb.education.com/game/am-and-pm-quiz/

13

Week 7

Measurement and Line Plots Rationale for Sequence Prior Knowledge

• Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch

• Create a number line that is marked off in whole numbers, halves, and fourths (including mixed numbers) based on the data collected

• Show the data by making a line plot

Separating ½ in from ¼ in allows the students time to become proficient in measuring to the nearest ½ in before adding another concept.

Once students have plotted fractions on a number line, they will revisit number lines to plot mixed numbers (incorporating both halves and fourths).

Creating line plots reinforces fraction equivalencies.

In second grade, students used rulers to measure to the nearest whole inch. They also created whole number line plots.

Standards

Resources

I Can Statements

3.MD.B.4 (SUPPORTING) Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units: whole numbers, halves, or quarters.

Academic Vocabulary: length, horizontal scale, line plot, halves, quarters (as they relate to measurement)


I can use a ruler to measure lengths in whole, half, and quarter (fourth) inches.

I can generate and record measurement data using whole, half, and quarter (fourth) inches.

I can create a line plot with a horizontal scale marked off in whole, half, or quarter (fourth) units.


14

Week 8

Meanings of Multiplication Rationale for Sequence Prior Knowledge

• Draw models and write story contexts to interpret total number of objects in equal groups and arrays

• Use multiplication to solve contextual problems within 100 in situations involving equal groups, arrays, and measurement quantities

Multiplication follows patterns because it connects to repeated addition, skip counting, and repeated addition equations. Multiplication is the third grade fluency standard, and this standard allows students to dig deeper into their understanding of multiplication and its inverse operation, division

In second grade, students built arrays and wrote repeated addition equations. This helps students connect repeated addition to multiplication.


3.OA.A.3 (MAJOR) Multiply and divide within 100 to solve contextual problems, with unknowns in all positions, in situations involving equal groups, arrays, and measurement quantities using strategies based on place value, the properties of operations, and the relationship between multiplication and division

(e.g., contexts including computations such as 3 x ? = 24, 6 x 16 = ?, ? ÷ 8 = 3, or 96 ÷ 6 = ?) (See Table 2 - Multiplication and Division Situations).

Academic Vocabulary: contextual problem, unknown number, computation

https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-mult-div-topic/1-digit-multiplication-division/v/unknowns-with-multiplication-and-division

https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-mult-div-topic/1-digit-multiplication-division/e/letters-and-symbols-in-multiplication-and-division-equations

I can represent multiplication and division word problems using drawings, concrete models, and equations with unknowns in all positions.

I can determine when to multiply and divide in word problems.

I can solve word problems involving equal groups, arrays, using drawing









15

Week 9

Time Rationale for Sequence Prior Knowledge

• Solve contextual problems involving addition and subtraction of time intervals in minutes

• Represent elapsed time problems with models such as a number line

Time follows addition and subtraction because students apply addition and subtraction strategies, such as counting up, counting back, and using number lines, to solve elapsed time problems.

In previous grades, students learned to tell time to the hour, half hour, quarter hour, and five minutes. In second grade, students notate a.m. and p.m. when recording time.

Standards

Resources I Can Statements

3.MD.A.1 (MAJOR) Solve contextual problems involving addition and subtraction of time intervals in minutes. For example, students may use a number line to determine the difference between the start time and the end time of lunch.

Academic Vocabulary: contextual problem, intervals of time

r

Dajuana’s Homework

https://www.illustrativemathematics.org/content-standards/3/MD/A/1/tasks/1989

Word Problems Time Intervals

https://www.k-5mathteachingresources.com/support-files/word-problems-time-intervals.pdf

http://www.sheppardsoftware.com/mathgames/time/mathman_time_elapsed.htm

I can create and solve addition and subtraction word problems involving durations of time measured in minutes (elapsed time). Students may use a number line to determine the difference between the start time and the end time of lunch.





http://www.sheppardsoftware.com/mathgames/time/mathman_time_elapsed.htm

16

Week 10

Multiplication Properties and Multiplying by Multiples of 10

Rationale for Sequence Prior Knowledge

• Use the distributive property of multiplication

• Multiply numbers by multiples of 10.

Adding the distributive property here allowed the students time to learn to use the other properties of multiplication properly. Learning the distributive property will also help them be ready for the next step in finding area of rectangles.

Earlier in the year students were introduced to the following properties: zero, identity, commutative and associative. Now that they have a good understanding of those properties we will add in the distributive property.

Students have a good understanding of number patterns and also should know most of their multiplication facts 0-9.


3.OA.B.5 (MAJOR) Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (Associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (Distributive property of multiplication over addition).

3.NBT.A.3 (SUPPORTING) Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

Academic Vocabulary: multiples of 10

http://www.talesfromoutsidetheclassroom.com/2015/07/introducing-the-distributive-property.html#_a5y_p=4281080

https://video.search.yahoo.com/yhs/search?fr=yhs-iba-1&hsimp=yhs-1&hspart=iba&p=distributive+property+of+multiplication+video+for+kids#id=1&vid=548ad973089f7dc2533eec0f46b6f922&action=click

http://www.math-play.com/math-basketball-properties-of-multiplication/math-basketball-properties-of-multiplication-game_html5.html

I can distinguish between the properties of multiplication.

I can apply the properties of multiplication to solve problems more efficiently.

I can justify my thinking using algebraic properties as proof.

I can explain the commutative, associative, and distributive property of multiplication.

I can apply the commutative, associative, and distributive properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.











17




Multiplication Strategy: Using Known Facts to Solve Other Facts

Multiplication Strategy: Associative Property for Multiplying Multiples of Ten

Multiplication Strategy: Breaking Factors into Smaller Factors Division Strategy: Partial Quotients

Contextual Problem Topics (Tuesdays and Thursdays)

3.OA.D.9 All operations, area, metric measurement, and problems with multiple parts

Week 1

Division Rationale for Sequence Prior Knowledge

• Draw models and write story contexts to interpret division as grouping or sharing

• Find the answer to a division problem as an unknown factor problem

Division follows multiplication because students can apply what they have learned about multiplication to solve division problems.

Earlier this year, students learned about equal groups and arrays to solve multiplication problems.


3.OA.A.2 (MAJOR) Interpret the dividend, divisor, and quotient in whole number division equations (e.g., 28 ÷ 7 can be interpreted as 28 objects divided into 7 equal groups with 4 objects in each group or 28 objects divided so there are 7 objects in each of the 4 equal groups).

3.OA.B.6 (MAJOR) Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Academic Vocabulary – dividend, divisor, quotient, equation, equal, unknown-factor

http://www.ashleigh-educationjourney.com/wp-content/uploads/2013/11/DSC010622.jpg


I can explain division as a set of objects partitioned into an equal number of shares or groups.

I can describe a context in which a number of shares or a number of groups can be expressed by dividing or as division.

I can identify parts of division equations (dividend, divisor, and quotient).

I can illustrate quotients in relation to divisors and dividends (e.g. 56 ÷ 8=7) can be interpreted as 56 objects divided into 8 equal groups or 56 objects divided so there are 8 in each group) as in bar modeling.

I can describe the inverse relationship between multiplication and division.






18

Week 2


• Use dimensions of rectangles to solve area problems by multiplying side lengths

By this time most students are proficient in multiplying and have a good understanding of how tiling can be related to multiplication to find area.

Students have prior knowledge from earlier this year when they learned to find area using square units.


3.MD.C.7 (MAJOR) Relate area of rectangles to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning

Academic Vocabulary – area, rectangles, operations, side, lengths, whole-number

https://www.math-salamanders.com/image-files/3rd-grade-math-worksheets-area-2.gif

https://www.math-salamanders.com/image-files/area-worksheet-area-3.gif

http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/AreaShapesShoot.htm

I can find the area of a rectangle by multiplying its length by its width.

https://www.math-salamanders.com/image-files/3rd-grade-math-worksheets-area-2.gif

https://www.math-salamanders.com/image-files/area-worksheet-area-3.gif

http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/AreaShapesShoot.htm

19

Weeks 3-4

Liquid Volume and Mass Rationale for Sequence Prior Knowledge

• Measure the mass of objects and liquid volume

• Estimate the mass of objects and liquid volume using benchmarks

• Solve one-step problems adding and subtracting within 1000 and multiplying and dividing within 100

Students continue to use the four operations to solve one-step contextual problems now involving milliliters, liters, kilogram, and grams.

I n kindergarten, students described measurable attributes of objects. In first and second grade, students described, measured, estimated, and compared lengths using nonstandard units and standard units of measure.


3.MD.A.2 (MAJOR) Measure the mass of objects and liquid volume using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l) . Estimate the mass of objects and liquid volume using benchmarks. For example, a large paper clip is about one gram, so a box of about 100 large clips is about 100 grams. Therefore, ten boxes would be about 1 kilogram.

Academic Vocabulary – mass, liquid volume, standard units, grams, kilograms, milliliters, liters, estimate, benchmarks

The Orange

https://gfletchy.com/the-orange/

Bubble Gum Activity

https://www.teachengineering.org/activities

/view/duk_bubble_mary_act

I can use the four operations to solve one- and two- step word problems involving mass and volume that are given in the same units.

I can estimate the liquid volume using liters.

I can estimate the mass of objects using grams and kilograms.

I can tell if an estimation is reasonable.

I can use drawings to represent objects and units too large to measure.





https://www.teachengineering.org/activities/view/duk_bubble_mary_act



20

Week 5

Measurement and Line Plots Rationale for Sequence Prior Knowledge

• Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch

• Create a number line that is marked off in whole numbers, halves, and fourths (including mixed numbers) based on the data collected

• Show the data by making a line plot

By this time students should be proficient at measuring to the nearest ½ in.

Students learned earlier this year how to measure to the nearest ½ in.

Standards

Resources

I Can Statements

3.MD.B.4 (SUPPORTING) Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units: whole numbers, halves, or quarters.

Academic Vocabulary – lengths, rulers, halves, fourths, line plot, horizontal, whole numbers, quarters

https://www.funbrain.com/games/measure-it

https://learnzillion.com/lesson_plans/6360-measure-to-the-nearest-half-inch-and-quarter-inch/

https://www.schooltube.com/video/d43e7738596540f9873d/

I can use a ruler to measure lengths in whole, half, and quarter (fourth) inches.

I can generate and record measurement data using whole, half, and quarter (fourth) inches.

I can create a line plot with a horizontal scale marked off in whole, half, or quarter (fourth) units.

https://www.funbrain.com/games/measure-it



https://www.schooltube.com/video/d43e7738596540f9873d/

21

Weeks 6-7


• Use area models to represent the distributive property

• Decompose rectilinear figures into non-overlapping rectangles and add the areas together

• Use multiplication and division to solve contextual problems within 100 in situations involving arrays and measurement quantities


3.MD.C.7 (MAJOR) Relate area of rectangles to the operations of multiplication and addition.

c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. For example, in a rectangle with dimensions 4 by 6, students can decompose the rectangle into 4 x 3 and 4 x 3 to find the total area of 4 x 6. (See Table 3 - Properties of Operations)

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

Academic Vocabulary – area, rectangles, multiplication, addition, tiling, concrete case, side lengths, distributive property, decompose, additive, rectilinear, non-overlapping

https://learnzillion.com/lesson_plans/5289-use-area-models-to-represent-the-distributive-property/

http://cupcakesncurriculum.blogspot.com/2015/01/teaching-distributive-property-using.html

https://video.search.yahoo.com/yhs/search?fr=yhs-itm-001&hsimp=yhs-001&hspart=itm&p=using+the+distributive+property+to+find+area+of+rectangle#id=2&vid=c637f6a8fa92eac0bf8cf03b4ea89d8a&action=click

https://www.math-salamanders.com/image-files/math-worksheets-4th-grade-area-6.gif

I can demonstrate that the sum of the unit tiles that fit inside a rectangle and the product of the length and width of that rectangle are the same.

I can find the area of a rectangle using tiles and relate it to the area model of multiplication.

I can use area models to explain the distributive property.

I can recognize that areas of each rectangle in a figure made of straight lines can be added together to find the area of the figure.

I can find the area of rectangular figures by decomposing (separating) the figure and adding the area of the separated figures together.

I can decompose an irregular figure into non-overlapping rectangles.

I can explain area as additive (by adding two angles measured together) and use this understanding to solve word problems.












22

Weeks 8-9

Geometry Rationale for Sequence Prior Knowledge

• Determine if a figure is a polygon by its attributes

• Understand shapes have different categories based on geometric attributes

• Recognize rhombuses, rectangles, and squares as examples of quadrilaterals

• Draw examples of quadrilaterals that do not belong to any of the subcategories listed above

Students have a great deal of background knowledge about shapes and it is a supporting category which should make it easier for them to pick quickly at this point in the year.

In second grade, students recognized and drew shapes with specified attributes (such as the number of angles, corners, and sides). Students gained knowledge of circles, triangles, quadrilaterals (squares, rectangles, and trapezoids), pentagons, and hexagons.


3.G.A.1 (SUPPORTING) Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories.

3.G.A.3 Determine if a figure is a polygon.

Academic Vocabulary – attributes, rhombuses, rectangles, squares, quadrilaterals, polygon

https://www.k-5mathteachingresources.com/support-files/shape-match.pdf

https://i.pinimg.com/736x/07/16/8e/07168e2ccbd098e9eba17adc4864fb8e.jpg

I can identify and determine two-dimensional shapes based on their attributes.

I can identify rhombuses, rectangles, and squares as quadrilaterals.

I can describe, analyze, and compare properties of two-dimensional shapes.

I can compare and classify shapes by attributes, sides, and angles.

I can group shapes with shared attributes.

(3.G.A.3) - Refer to 3.G.A.1





23




Fractions: Naming Fractions of a Region or Area

Fractions: Naming Fractions on a Number Line

Fractions: Comparing and Ordering

Contextual Problem Topics (Tuesdays and Thursdays)

Review of all types of contextual problems

Weeks 1 and 2

Graphs Rationale for Sequence Prior Knowledge

• Solve one- and two-step “how many more” and “how many less” problems

• Draw scaled pictographs and bar graphs

Graphing follows two-step contextual problems and multiplication/division so that students can create and interpret scaled pictographs and bar graphs.

In first and second grade, students read and created single unit bar and pictographs. First and second graders solved one-step “how many more” and “how many less” problems related to the data in a graph.


3.MD.B.3 (SUPPORTING) Draw a scaled pictograph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled graphs.

Academic Vocabulary – pictograph, bar graph, data set

http://www.commoncoresheets.com/Math/Bar%20Graphs/5%20Bars/English/1.pdf

https://nces.ed.gov/nceskids/createagraph/default.aspx?ID=9069bd5b498c42adaca010e5bd275707

https://video.search.yahoo.com/yhs/search?fr=yhs-itm-001&hsimp=yhs-001&hspart=itm&p=how+to+make+a+pictograph+video+for+kids#id=6&vid=76621c361e31c19d132889ea7b40c5b1&action=click

http://www.commoncoresheets.com/Math/PictoGraphs/Reading%20E/English/3.pdf

I can read and interpret scaled bar graphs in order to solve one-and two-step "how many more" and "how many less" problems.

I can choose a proper scale for a bar graph or picture graph.

I can create a scaled picture graph or bar graph with several categories to represent data (e.g. one square in a bar graph or one picture might represent 5 objects.)











24

Weeks 3, 4, and 5

TN Ready Review and Flex Time (snow or sick days) Rationale for Sequence Prior Knowledge

We left these three weeks open to either use for

TN Ready Review of the things your students

struggle with according to your assessments or as

days that lessons can be pushed to if we miss

school days for illness or weather.


State of Tennessee TN Ready Prep

grade 3 math pacing guide -...

Documents