Mathematics Unit 3: Multiplication and Division; Number Sentences and Algebra
October 8–November 6, 2013
Inquiry Question:
Why is one neither prime nor composite?
Essential Learning Goals:
- Interpret multiplication equations as comparisons and represent multiplicative comparisons as multiplication equations (for example, 35 = 5 x 7 as 35 is five times as many as seven and seven times as many as five). (ELG.MA.4.OC2)
- Solve multi-step word problems using the four operations. Represent these problems using equations with letters standing for unknown quantities. (ELG.MA.4.PFA2)
- Find all factor pairs for whole numbers in the range 1–100. Recognize that whole numbers are multiples of each of their factors; determine whether given numbers are multiples of given one-digit numbers; determine whether given whole numbers in the range 1–100 are prime or composite. (ELG.MA.4.NN3)
- Generate number or shape patterns that follow given rules. Identify apparent features of patterns not explicit in the rules themselves (ELG.MA.4.PFA1)
Concepts:
Factoring, multiplication, division
Academic Vocabulary: Right-click on vocabulary to look it up in the dictionary.
Solve, represent, multiply, divide, add, subtract, assess, unknown, variable, classification
Technical Vocabulary: Right-click on vocabulary to look it up in the dictionary.
Factor, whole number, remainder, product, multiple, natural numbers, counting numbers, mental strategies, estimation, reasonableness, word problems, prime, composite, algorithms, equations, rectangular arrays, area models
Technology:
Stamps: http://www.fisme.science.uu.nl/toepassingen/03299/ (computation in groups; multiplication with arrays)
Product Game: http://illuminations.nctm.org/ActivityDetail.aspx?ID=29 (fluency with multiplication of numbers 1–9)
Factorize: http://illuminations.nctm.org/ActivityDetail.aspx?ID=64 (dividing numbers into two factors and building arrays to represent each factorization)
Product Game: http://illuminations.nctm.org/ActivityDetail.aspx?ID=29 (fluency with multiplication of numbers 1–9)
Factorize: http://illuminations.nctm.org/ActivityDetail.aspx?ID=64 (dividing numbers into two factors and building arrays to represent each factorization)
Common Misconception:
When listing multiples of numbers, students do not list the number itself. Emphasize that the smallest multiple is the number itself.
Students think larger numbers have more factors. Instruct students to share all factor pairs and ask them how they found the pairs.
Students think larger numbers have more factors. Instruct students to share all factor pairs and ask them how they found the pairs.