East Saint Louis District 189 Math Curriculum Grade 3
Sequence of Grade 3 Modules Aligned with the Standards
- Module 1: Numbers to 10,000
- 10 Days
- Module 2: Mental Math and Estimation
- 11 Days (incl. benchmark assessment)
- Module 3: Addition to 10,000
- 8 Days
- Module 4: Subtraction to 10,000
- 8 Days
- Module 5: Using Bar Models: Addition and Subtraction
- 8 Days (incl. benchmark assessment)
- Module 6: Multiplication Tables: 6, 7, 8 & 9
- 14 Days
- Module 7: Multiplication
- 10 Days (incl. benchmark assessment)
- Module 8: Division
- 9 Days
- Module 9: Using Bar Models: Multiplication and Division
- 13 Days (incl. benchmark assessment)
- Module 14: Fractions
- 13 Days
- Module 11: Metric Length, Mass, Volume
- 8 Days
- Module 12: Real-World Problems: Measurement
- 7 Days (incl. benchmark assessment)
- Module 19: Area and Perimeter
- 11 Days
- Module 13: Bar Graphs and Line Plots
- 9 Days (incl. benchmark assessment)
- Module 16: Time and Temperature
- 4 Days
- Module 17: Angles and Lines
- 2 Days
- Module 18: Two Dimensional Shapes
- 10 Days
- Module 10: Money
- 9 Days
- Module 15: Customary Length, Weight and Capacity
- CCSS calls for volumes and masses using metric measurement
Summary of Year
Third Grade mathematics is about (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
Key Areas of Focus for 3-5: Multiplication and division of whole numbers and fractions—concepts, skills, and problem solving
Required Fluency: 3.OA.7 Multiply and divide within 100.
3.NBT.2 Add and subtract within 1000.
CCSS Major Emphasis Clusters
Operations and Algebraic Thinking
- Represent and solve problems involving multiplication and division.
- Understand the properties of multiplication and the relationship between multiplication and division.
- Multiply and divide within 100.
- Solve problems involving the four operations and identify and explain patterns in arithmetic.
- Develop understanding of fractions as numbers.
- Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Rationale for Module Sequence in Grade 3
In Grade 2, students learned how to count read and write numbers up to 1000. In Module 1, students will learn to count, read and write numbers up to 10,000. Base-ten blocks are used to develop the association between the physical representation of the number, the number symbol and the number word. Students should see multiple representations using place-value charts and strips showing thousands, hundreds, tens and ones. Students will identify the place value of each digit in a number and be able to express numbers in standard and expanded form. Students will compare numbers using least and greatest and order sets of numbers in increasing and decreasing order. Students will apply these skills to fill in missing numbers in patterns and on number lines.
Module 2 will focus on building students’ number sense regarding place value concepts. The strategies used in this module focus on composing and decomposing numbers and the use of number bonds.
In 2nd grade, students learned addition up to 1000 with or without regrouping along with concrete representations to help them visualize the regrouping. In Module 3, students will learn to add 4-digit numbers with or without grouping using base-ten blocks and place-value charts. They are also introduced to larger numbers that have a thousands place. Students will transfer the skills from their work with 3-digit numbers to their work up to 10,000. Students will solve real-world application problems involving addition.
In Module 4, students will build on their work from 2nd grade where they worked with subtraction up to 1000 with and without regrouping. They will continue to use base-ten blocks and place value-charts to visualize subtraction with regrouping. Students will recognize the same strategies that were used with numbers to 1000 can be extended in this module. Real-world problems involving subtractions will be solved. Students will also realize that addition and subtraction are inverse operations and that subtraction problems should be checked using addition.
Students will begin Module 5 by reviewing how to solve two step real-world problems. Bar models will be used to illustrate part-whole, comparison, or both in order to solve real-world problems involving addition and subtraction. Drawing models helps students to visualize and construct concrete pictures to help make sense of problems. Students must understand the mathematical concepts within the problem and this equips them with a strong conceptual foundation.
Students learned in Grade 1 the meaning for equal groups for the beginning of multiplication and division. They continued in Grade 2 by learning repeated addition for multiplication and division to be sharing or grouping. They also learned the multiplication facts for 2, 3, 4, 5 and 10. In Module 6, these concepts are reviewed and extended to the facts of 6, 7, 8, and 9. They will also learn that multiplication and division are inverse operations and division can be used to find a missing factor. Both multiplication and division are associated with the part-whole concept and the conceptual link between multiplication and division are strengthened. The real number properties that students used with addition are extended to multiplication: Commutative Property of Multiplication and Associative Property of Multiplication. Students will learn two new properties: Multiplicative Property of One and Multiplicative Property of Zero.
Students have learned several strategies and concepts for multiplication in Grades 1 & 2. In Module 7, these concepts are reviewed and extended to 3-digit multiplication. Students will use the following methods to multiply: mental multiplication, multiplying without regrouping and multiplying with regrouping. The Properties of Multiplication are applied in multiplying 2-and 3-digit numbers by a 1-digit number. Students will use place value to them multiply numbers in vertical form. These concepts and strategies will be applied in solving real-world problems.
Students have learned in Grade 2 and earlier in Grade 3 that there are two division situations: sharing and grouping. They also learned division as repeated subtraction or the related multiplication facts. By now, students should know multiplication facts 2 – 10 well enough to divide mentally. In Module 8, division concepts are extended to division situations where there might be remainders. Students realize that the dividend does not always divide exactly into equal groups. Students also learn to apply division strategies to 2-digit numbers. Vertical division form is used to divide 2-digit number by finding and subtracting partial products.
Bar models will be extended for use in multiplication and division problems in Module 9. Both multiplication and division are based on the concept of equal groups, or the part-whole concept, where each equal group is one part of a whole. In 2nd grade, students used the unitary bard model to represent situations where a set of objects was grouped equally into new sets. The bar model will also be used in two step problems or to compare two sets of objects. Drawing bar models will provide students with a systematic means of organizing information determining the calculations necessary to solve a problem.
In Grade 2, students were introduced to thefractions halves, thirds, and fourths for the first time and how to relate equal parts to a whole using fractional notation. They used models to add, subtract and compare fractions with like denominators. In Module 14, students will work with fractions of wholes that are divided into more than 4 equal parts. Students will learn new concepts such as equivalent fractions and identifying a fractional part of a set. Students will develop an understanding of the meanings and uses of fractions. Students learn to read, write and identify fractions of a set and then find the relating number of items. Pictures should be used extensively to represent real-world problems.
Previously, students estimated, measured and compared lengths to the nearest centimeter and meter. In Module 11, students will now learn how to express measures using compound units involving meters and centimeters and how to convert from one metric unit of length to another. Students will add the measures of kilometers, kilograms, grams and milliliters into their base of knowledge. They will use these measurements to measures actual items and convert between units of measure.
In Module 12, students will use the conversions they learned in the last module to solve real-world problems. Students will use bar models to organize the information in a problem and solve one-and two-step problems. The part-whole concept can be used to think about number relationships. Students are moving to drawing the bar model to solve real-world problems without teacher assistance by the end of Grade 3.
Students learned to multiply with the visual area model in Module 6. This skill enables students to multiply efficiently to find the area of figures. Students will combine geometry and measurement to learn the concepts of area and perimeter. Students will express answers with the appropriate units. They will also choose appropriate units to measure area and perimeter of figures of different sizes. Students will be encouraged to explore and understand units used to find perimeter and are of figures and analyze the relationship between them. Students will apply the concepts of area and perimeter to solve real-world problems, especially those objects they encounter in everyday life.
Students will be introduced to line plots and learn more about bar graphs in Module 13. Students will use bars drawn against a scale to show data and that bar graphs can be used to make comparisons. Students will work with scales in skips of two or greater. They will learn how to read and interpret bar graphs to solve real-world problems. Students will learn to use line plots to organize data and show the frequency of an event. Students will construct line plots from data presented in a table without the use of a tally chart.
In Grades 1 & 2, students learned to tell time within 5 minutes and the correct notation for representing the time of day. Students will extend their learning in Module 16 to learn about reading and telling time to the nearest minute. Students are taught to convert time units in hours and minutes and to add and subtract time. They will learn that time can be used to find out when activities start and end and how long an activity might last. Students will be introduced to the concept of temperature in conjunction with reading a Fahrenheit thermometer and solve real-world problems involving temperature.
In 2nd grade, students learned to distinguish between lines and curves. This is the foundation for students to recognize angles, perpendicular lines, and parallel lines in Module 17. Students will compare angles relative to right angles in preparation for the work of angle measures in Grade 4. The terms angle, perpendicular lines and parallel lines should be related to real-life objects as often as possible. Students should see these elements in plane shapes and three-dimensional objects.
In Module 18, students will use previous concepts and skills in order to identify the sides and angles of closed polygons. They will learn to classify polygons and name the shapes. Students will learn about the concept of congruency and how to check for congruency. Students will also determine whether or not figures are symmetric and if plane shapes contain a line of symmetry. Students should link polygons, quadrilaterals, congruent figures and symmetric figures with everyday objects. This knowledge will enable them to appreciate the usefulness of their mathematical skills.
The concepts of money are reviewed in Module 10 and extended to amounts up to $100. The focus in Grade 3 is to equip students with mental strategies in adding and subtracting the symbolic form of money. Number bonds can be used to link prior knowledge with this new set of skills. The use of bar models to solve real-world problems is used to reinforce students’ understanding.
Throughout Grade 3, students will slowly build up to a rectangular array area model using hands-on rectangular arrays (i.e., a Rekenrek) and/or pictures of rectangular arrays involving objects only (stars, disks, etc.)—all in the context of learning multiplication and division. This work is necessary because students initially find it difficult to distinguish the different squares in a rectangular array area model (the third array in the picture below), count them and recognize that the count is related to multiplication. See progression below:
Alignment Chart
Module and Approximate Number of Instructional Days/ Common Core Learning Standards Addressed in Grade 3 Modules and Notes / Vocabulary / Notes and Instructional Strategies / Performance Based Tasks/Formative/ Summative Assessments/Notes
Module 1: Numbers to 10,000(10 days)
M.P. 1
M.P. 4
M.P. 5
M.P. 7
Keep the chapter to the specific days of the chapter planning guide! /
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.D.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends
Focus on the patterns in this chapter. The patterns will help build to 3.NBT.A.1 and 3.NBT.A.2.
/- Word form,
- Standard form,
- Digit,
- Place-value chart,
- Place-value strips, Expanded form,
- Greater than,
- Less than, Rule,
- Number Line
- Decomposing
- Composing
How many tens are in . . . 10, 100, 1000, 10,000?
How many hundreds are in . . . 100, 1000, 10,000?
Extend questions - How many hundreds are in 4000? How many tens are in 4000? How many ones are in 4000?
Keep writing in expanded notation with words also, breaking up the number in different ways. As the lessons progress, keep asking what is 10 more than, 100 more than, 1000 more than the given number. Include the skip counting.
Tools - Number lines, Place value charts, place value strips, place value discs if available.
Use skip counting by 10, 100, 1000 from any given number. Strategies – Line number vertically to compare numbers and skip counting. Start with 256 and count by 10's ten times. Where did you end up? What did you add to 256? You can do this backwards also.
Write number sequences - start with 3091 and show 5 terms in the sequence - increase by 10's, decrease by 100's.
Games –place value war with cards; Hands-on Activity page 25 (use cards to get the numbers) / Formative Assessments – Number Talks to do single digit addition and subtraction focusing on making tens and doubles strategies. Moe to double digit addition problems.
Performance based tasks - Use white boards or exit tickets to assess their ability to decompose numbers into different place value units – 3,467 can be 3 thousands, 4 hundreds, 6 tens, 7 ones; 2 thousands 14 hundreds 15 tens, 17 ones, etc. Ask how many ways can you rename 3,467 as the sum of smaller numbers?
Put on Your Thinking Cap
Assessment – Test Prep 1
Module 2:
Mental Math and Estimation
(11 days—including 1 Day for benchmark assessment)
M.P. 1
M.P. 5
M.P. 8
Lesson 2-4 focuses on 3.OA.D.8 – 2-day lesson. Keep to pacing of remaining lessons. /
Use place value understanding and properties of operations to perform multi-digit arithmetic.
3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.A.2Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. A range of algorithms may be used.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.3.OA.D.8 Solve two-step word problems using the four operations. 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. / Rounded,
Reasonable,
Estimate,
Overestimate,
Leading digit,
Front-end estimation / Students should be fluent with decomposing two digit numbers, i.e. 48 = 50 – 2 or 48 = 40 + 8. Do number talks where students have to decompose two digit numbers in as many ways as possible. Strategies to continue are making tens and doubles, so they can compensate from there. If students are having troubles with making tens, do some Number Talks like 6 + 3 + 4; 7 + 2 + 8; 7 + 5 + 3 + 3; to practice finding tens. Do the same with double facts. Important to have students discover when adding two 2-digit numbers, that both numbers do not need to be decomposed into place value. 34 + 23 can be added as 34 + 20 then add 3 more. Some two digit problems may be easier to decompose into place value units when there is no regrouping.
For subtraction, have students discover that you can decompose just the subtrahend (second number) to make it easier to subtract. For example, 87 – 34 = 87 – 30 – 4. Breaking into place value units will be just like partial sums.