Mathematics Unit 5: Big Numbers, Estimation, and Computation
December 16, 2013–January 23, 2014
Inquiry Question:
- Why don’t we classify decimals or fractions as prime or composite?
Essential Learning Goals:
- Interpret multiplication equations as comparisons and represent multiplicative comparisons as multiplication equations (for instance, 35 = 5 X 7 as 35 is five times as many as seven and seven times as many as five). (ELG.MA.4.OC2)
- Use equations, arrays, and area models to represent multiplication and division. (ELG.MA.4.OC7)
- Solve multi-step word problems using the four operations. Represent these problems using equations with letters standing for unknown quantities. (ELG.MA.4.PFA2)
- Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on place value meaning using >, <, and = symbols. (ELG.MA.4.NN1)
- Use place value understanding to round multi-digit whole numbers to any place. (ELG.MA.4.OC6)
- Multiply whole numbers of up to four digits by one-digit whole numbers and multiply two, two-digit numbers. Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors. (ELG.MA.4.OC3)
Concepts:
Factoring, multiplication, estimation, multiplicative and additive comparisons, distributive property, partial products, area models
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, remainder, whole numbers, product, multiple, mental strategies, estimation, rounding, reasonableness, word problems, multiplicative comparison, algorithms, equations, rectangular arrays, area models
Technology:
- Rectangle Multiplication: http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html?from=search.html?qt=circle+21 (visualize multiplying two numbers as an area)
- Rectangle Division: http://nlvm.usu.edu/en/nav/frames_asid_193_g_2_t_1.html?from=search.html?qt=circle+21 (visualize and practice dividing numbers using area representations)
Common Misconception:
Students commonly misinterpret “B is 3 more than A” and “B is 3 times as much as A” in multiplicative comparisons. Visual models help students avoid these problems.