3rd Grade Math Instructional Focus Units



Instructional Focus UnitsEstimated TimeFocus 1Introduction to Multiplication and Division5 WeeksFocus 2Applying Place Value, Properties and Operations to Add/Sub Multi- Digit Numbers4 WeeksFocus 3Develop Understanding of Fractions as Numbers5 WeeksFocus 4Develop Understanding of Multiplication and Division5 WeeksFocus 5Demonstrating Computational Fluency in Problem Solving 2 WeeksFocus 6Extending Understanding of Multiplication & Division/Attributes of Geometric Figures 4 WeeksFocus 7Connecting Data to the Four Operations and Fractions 4 WeeksFocus 8Extending Understanding of Fractions as Numbers 3 WeeksFocus 9Understanding measures of Liquid Volume, Weight and Mass. 3 Weeks***Based on the standards, not all lessons within the resource may be needed to meet the needs of your students. Focus 1: Introduction to Multiplication and DivisionStudents begin developing these concepts by working with numbers with which they are more familiar, such as 2s, 5s, and 10s, in addition to numbers that are easily skip counted such as 3s and 4s. Since multiplication is a critical area for grade 3, students will build on these concepts throughout the year, working towards fluency by the end of the year. HYPERLINK ""Standards3.OA.A.13.OA.A.23.OA.A.33.OA.A.43.OA.B.53.OA.B.63.OA.C.73.OA.D.83.OA.D.93.MD.C.7Estimated Time5 weeks Principal Resource-Fosnot Grocery Stamps and Measuring StripsAND-IDS Unit 5, including Common Core Resource 3.1A, 3.5A, 3.5B, 3.7AAdditional ResourceRoutines- -Use mini-lesson in Grocery Stamps & Measuring Strips-Routines in addition to Ten-Minute math: word problems -equal groups unknown product, -Fosnot mini-lessons Early Mult/Div. A1 – A10 Notes**Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 Fluently –Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking.3.NBT.A.2 Add/Subtract within 1000Focus 2: Applying Place Value, Properties and Operations to Add/Sub Multi- Digit NumbersIn this focus students increase the sophistication of computation strategies that include place value understanding for addition and subtraction within 1,000. The concept of rounding is introduced to offer the students another strategy to judge the reasonableness (MP.3) of their answers in addition and subtraction situations. Standards3.OA.D.83.OA.D.93.NBT.A.13.NBT.A.23.MD.A.1 Estimated Time4 weeksPrincipal ResourceIDS Unit 3 - Include Common Core IDS Book, sessions 1.7A and EXCLUDE session 3.1Principal resource for 3.MD.A.1 Engage NY – Module 2, Topic A, lessons 1-5 Additional Resource-3.NBT.A.1 – Engage NY – Module 2, Topic C, lesson 14 RoutinesIn addition to Ten-Minute math -Fosnot Mini-lessons in Extending add. & sub. B1-B15-Number Talks pg. 186-196-Problem solving: Add To (Join, Result Unknown) Take from (Separate, Result Unknown), Put Together/Take Apart (Part-Part-Whole) and Compare problems. Refer to Table 1, p. 21 (in 2nd grade CCSS). Problems into the 1,000’s for add. & sub. Include multi-step word problems. Notes**Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Focus 3: Develop Understanding of Fractions as NumbersStudents have had experience partitioning shapes into fair shares (1.G.3 and 2.G.3) using words to describe the quantity. In this focus students extend this understanding to partition shapes and number lines representing these fair shares using fraction notation. Students learn to view unit fractions as building blocks-understating that every fraction is an iteration of unit fractions. (2/3 = 2 pieces of size one-third)Standards3.NF.A.13.NF.A.23.NF.A.3 3.G.A.2Estimated Time5 weeksPrincipal ResourceEngage NY Module 5 Topic A, B, & C ANDIDS Unit 7 Investigations 1 & 2Additional Resource -In addition to Ten-Minute math: Problem solving with strong emphasis on fractions in real world context-Number Talks pgs. 197-216.NotesStudents develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. **Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Focus 4: Develop Understanding of Multiplication and Division This focus provides students a solid foundation in solving problems with equal groups and arrays. This is necessary to support future success with measurement problems. It includes multiple experiences to explore the connections between distributive property and multiplying the side lengths to determine area. Students recognize that multiplication strategies can be used to make sense of and solve division problems. Standards3.OA.A.33.OA.A.43.OA.B.53.OA.C.73.OA.D.83.OA.D.93.MD.C.73.NBT.A.3Estimated Time5 weeksPrincipal ResourceFosnot Muffles and Truffles ANDEngage NY Module 3, Topic A, B, C, D, E, & F Additional Resource- 3rd-grade-number-activities.html -Fosnot mini-lessons from Muffles and Truffles-Problem solving refer to CCSS pg. 29 Arrays/area- (unknown product- group size unknown- number of groups unknown).NotesDuring Muffles Truffles make sure to use the term AREA where applicable. Make the connection of multiplication and area. **Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently – Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking.3.NBT.A.2 Add/Subtract within 1000Focus 5: Demonstrating Computational Fluency in Problem SolvingStudents will focus on problems solving in order to demonstrate fluency with addition and subtraction to 1,000. Include two-step word problems.Standards3.OA.A.33.OA.C.73.OA.D.83.OA.D.93.NBT.A.2Estimated Time2 weeksPrincipal ResourceIDS Unit 8 Teacher links two-step word problems Additional Resource addition to Ten-Minute math- Problem solving refer to CCSS 2nd grade pg. 22 compare - difference unknown. Problem solving refer to CCSS 3rd grade pG.A.29 compare unknown product, group size unknown, and number of groups unknown. **2 step word problems must be incorporated**Notes**Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Focus 6: Extending Understanding of Multiplication & Division/Attributes of Geometric FiguresStudents will focus on reasoning with shapes and their attributes, including area and perimeter. The standards in this focus strongly support one another because perimeter, like area, is an attribute of shape. The focus extends student’s understanding of multiplication and division.Standards3.MD.C.53.MD.C.63.MD.C.73.MD.D.83.G.A.1Estimated Time4 weeksPrincipal ResourceIDS unit 4 EXCLUDE investigation 2Engage NY Module 4, Topics A, B, C & DAdditional ResourceRoutinesIn addition to Ten-Minute math- Fosnot Mini-lessons Extending Add & Sub. C7-C12-Continue problem solving for add/sub. within 1000's or mult/div within 100 **2 step word problems must be incorporated**-Number Talks pg. 278-285.NotesStudents recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. **Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Focus 7: Connecting Data to the Four Operations and FractionsIn this focus students will represent and interpret data in various formats (line plot, tables and bar graphs, etc…) that includes measurement of lengths with whole numbers and fractions. Students will solve one and two step “how many more” and “how many less” problems using the date presented in these graphs.Standards3.MD.B.33.MD.B.43.OA.A.33.OA.C.73.OA.D.83.OA.D.93.NBT.A.2Estimated Time4 weeksPrincipal Resource-IDS Unit 2 Include Common Core Book, session 2.3A and exclude sessions 2.3 - 2.74.MD.B.4 - Engage NY Module 6, Topic B Additional Resource addition to Ten-Minute math- Fosnot mini-lessons extended Add and Sub. C24-C32 -Problem solving into the 1,000’s for add. & sub. **2 step word problems must be incorporated** refer to Table 1, pg. 21 (in 2nd grade CCSS) problem solving using multiplication and division refer to pg. 29 in 3rd grade CCSS.Notes**Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Focus 8: Extending Understanding of Fractions as NumbersStudents will develop a conceptual understanding of equivalence. Multiple types of models and representations should be used to help students develop this understanding. Students will apply their understanding of equivalence to compare fractions. As a result students will develop conceptual understanding of fraction comparisons and practice reasoning about size. Students defend their reasoning and critique the reasoning of others using both visual models and their understanding of the structure of fractions.Standards3.NF.A.23.NF.A.3 3.G.A.2Estimated Time3 weeksPrincipal ResourceEngage NY Module 5 Topic D, E, & FAdditional ResourceTeaching Student Centered Mathematics 3-5 pgs. 131-152 2 step word problems. Integrate fractions into word problems (use the book Extending Children’s Mathematics Fractions and Decimals for word problems examples)NotesStudents are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.**Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Focus 9: Understanding measures of Liquid Volume, Weight and Mass. In this focus students will solve problems involving measurement and estimation of liquid volumes and masses of objects. Solve one-step word problems involving all four operations with grams, kilograms, liters, and milliliters given in the same units. Standards3.MD.A.23.NBT.A.13.NBT.A.2Estimated Time3 weeksPrincipal ResourceIDS Unit 9 - ONLY Common Core IDS Book, sessions 4A.1 - 4A.3 3.MD.2- Engage NY Module 2, Topic B Additional Resource addition to Ten-Minute Math--Problem solving involving masses and volumes that are given in the same unitsNotes**Because there are two principal resources listed in this focus unit, teachers need to determine the best sequencing for their population’s needs. Please note: not all lessons in every resource unit may be needed for every group of students. Please use your professional judgement when planning your instruction. End of the year 3rd grade fluency expectations – 3.OA.C.7 Multiply/Divide within 100 fluently - Rote memorization of basic facts is not fluency. Fluency with multiplication facts includes deeper understanding of concepts and flexible thinking. 3.NBT.A.2 Add/Subtract within 1000Table 1: Common addition and subtraction situations.6Result UnknownChange UnknownStart UnknownAdd toTwo bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?2 + 3 = ?Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. Howmany bunnies hopped over to the first two?2 + ? = 5Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?? + 3 = 5Take fromFive apples were on the table. I ate two apples. How many apples are on the table now?5 – 2 = ?Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?5 – ? = 3Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?? – 2 = 3Total UnknownAddend UnknownBoth Addends Unknown1Put Together / Take Apart2Three red apples and two green apples are on the table. How many apples are on the table?3 + 2 = ?Five apples are on the table. Three are red and the rest are green. How many apples are green?3 + ? = 5, 5 – 3 = ?Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?5 = 0 + 5, 5 = 5 + 05 = 1 + 4, 5 = 4 + 15 = 2 + 3, 5 = 3 + 2Difference UnknownBigger UnknownSmaller UnknownCompare3(“How many more?” version):Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?(“How many fewer?” version):Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have than Julie?2 + ? = 5, 5 – 2 = ?(Version with “more”):Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have?(Version with “fewer”):Lucy has 3 fewer apples than Julie. Lucy has two apples. How many apples does Julie have?2 + 3 = ?, 3 + 2 = ?(Version with “more”):Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?(Version with “fewer”):Lucy has 3 fewer apples than Julie. Julie has five apples. How many apples does Lucy have?5 – 3 = ?, ? + 3 = 56Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).1These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number as.2Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less than or equal to 10.3For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other versions are more difficult.Table 2: Common multiplication and division situations.7Unknown ProductGroup Size Unknown(“How many in each group?” Division)Number of Groups Unknown(“How many groups?” Division)3 x 6 = ?3 x ? = 18, and 18 ÷ 3 = ?? x 6 = 18, and 18 ÷ 6 = ?Equal GroupsThere are 3 bags with 6 plums in each bag. How many plums are there in all?Measurement example.You need 3 lengths of string, each 6 inches long. How much string will you need altogether?If 18 plums are shared equally into 3 bags, then how many plums will be in each bag?Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?If 18 plums are to be packed 6 to a bag, then how many bags are needed?Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?Arrays,4 Area5There are 3 rows of apples with 6 apples in each row. How many apples are there?Area example.What is the area of a 3 cm by 6 cm rectangle?If 18 apples are arranged into 3 equal rows, how many apples will be in each row?Area example.A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?If 18 apples are arranged into equal rows of 6 apples, how many rows will there be?Area example.A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?CompareA blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?Measurement example.A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost?Measurement example.A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?Measurement example.A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? GeneralGeneral a x ?b = ?a x ?? = p, and p ÷ ?a = ?? x ?b = p, and p ÷ ?b = ?7The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.4The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable.5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. ................
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