advertisement

Grade 3: Module 1 – Parent Letter What’s It All About? In this first module, students review addition and arrays and then begin to work with multiplication facts. The focus is on solving problems with the factors 2-5 and 10. The students then extend their work into division and its relationship to multiplication. This module will last for approximately 25 days. New or Recently Introduced Terms: Fact: 3 x 1 = 3, 3 × 2 = 6, 3 x 3 = 9 Factors: numbers that are multiplied together Repeated addition: adding equal groups together o 2+2+2+2 Multiplication/multiply: an operation showing how many times a number is added to itself o 5 × 3 =15 is the same as 5 + 5 + 5 =15 Size of groups: factor in a multiplication problem that refers to how many in a group Number of groups: factor in a multiplication problem that refers to the total equal groups Array: a set of numbers or objects that follow a specific pattern o an array with 3 rows and 4 columns Commutative Property: the order property; the order in which you multiply numbers does not change the sum of those numbers o rotate a rectangular array 90 degrees to demonstrate that factors in a multiplication sentence can switch places 3 x 4 = 12 4 x 3 = 12 Rotate: turn an array 90 degrees Equation: a number statement showing that 2 expressions are equal o 3 × 4 = 12 Distributive Property: break apart a larger number into 2 parts to make the multiplication easier; multiply each of the 2 parts by the other factor o 12 × 3 = (10 × 3) + (2 × 3) Divide/division: partitioning, or breaking, a total into equal groups to show how many equal groups add up to a specific number o 15 ÷ 5 = 3 Dividend: the total being divided o In 12 ÷ 3 = 4, the dividend is 12. Parentheses: ( ) used around a fact or numbers within an equation o (3 x 4) + (2 x 4) = 12 + 8 = 20 Quotient: the answer when one number is divided by another Unknown: the “missing” factor or quantity in multiplication or division Tape Diagram: a method for modeling problems 14 Number Bond: a method for showing a whole number divided into 2 parts Topic A: Students will understand equal groups of as multiplication, relate multiplication to the array model, and interpret the meaning of factors. Write multiplication sentences from equal groups. Relate multiplication to the array model. o 3 (number of groups) x 4 (size of the group) = 12 Interpret the meaning of factors. Number of groups: _6_ Size of each group: _3_ 6 x _3_= _18_ There are _18_ candies altogether. Topic B: Students explore division as an unknown factor problem. Understand the meaning of the unknown as the size of the group in division. Understand the meaning of the unknown as the number of groups in division. Interpret the unknown in division using the array model. o Rick puts 15 tennis balls into cans. Each can holds 3 balls. Use an array to model the problem. Topic C: Students begin to build fluency with facts of 2 and 3 using the array model and familiar skip-counting strategies. Practice related facts by skip-counting objects in array models. Find related multiplication facts by adding and subtracting equal groups in array models. o For example, 5 rows of 2 + 2 rows of 2 are easier to multiply than 7 rows of 2. o Also, 20 rows of 2 are easier to multiply than 18 rows of 2; so the students multiply 20 x 2 then subtract 2 rows of 2. Model the distributive property with arrays to decompose units as a strategy to multiply. Mid-Module Assessment: Read word problems involving multiplication/division, draw arrays to help solve the problem, and write number sentences showing the solution. Explain the use of Distributive Property. Topic D: Students solve two kinds of division situations—partitive (group size unknown) and measurement (number of groups unknown)—using factors of 2 and 3. The tape diagram is introduced as a tool to help students recognize and distinguish between types of division. o Rosie puts 2 lemon slices in each cup of iced tea. She uses a total of 8 slices. How many cups of iced tea does Rosie make? Tape diagram for measurement situation o Ms. Alves puts 21 papers in 7 piles. How many papers are in each pile? Tape diagram for partition situation Topic E: Students are introduced to multiplication by 4 through skip-counting objects in array models. Students revisit the commutative property, this time using both arrays and tape diagrams. They also examine the distributive property in greater depth. Skip-Count objects in models to build fluency with multiplication facts using units of 4. Relate arrays to tape diagrams to model the commutative property of multiplication. Use the distributive property as a strategy to find related multiplication facts. Model the relationship between multiplication and division. Topic F: Students model relationships between factors and decompose, or break apart, numbers as they further explore the relationship between multiplication and division. For example, students decompose 28 ÷ 4 as (20 ÷ 4) + (8 ÷ 4) = 5 + 2 = 7. Students apply the tools, representations, and concepts they have learned to problem-solving with multi-step word problems using all four operations. Apply the distributive property to decompose units. Solve two-step word problems involving multiplication and division. **End-of-Module Assessment: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division. o Knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. o 8 × ___ = 48 o 5 = ___ ÷ 3 o 6 × 6 = ___