Mathematics Unit 4: Decimals and Their Uses
November 7–December 13, 2013
Inquiry Questions:
- Is there a decimal closest to one? Why?
- What would change if we used a base-8 number system? What would our numbers look like?
Essential Learning Goals:
- Use decimal notation for fractions with denominators 10 or 100. (ELG.MA.4.NN5)
- Compare two decimals to hundredths by reasoning about their size. Record results of comparisons with symbols >, <, = and justify conclusions using visual models. (ELG.MA.4.NN6)
- Solve problems involving measurement and conversion of measurements from larger units to smaller units (including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec; in, ft, yd). (ELG.MA.4.MRF3)
Concepts:
Patterning, standard algorithm, addition, subtraction, place value, equivalent forms
Academic Vocabulary: Right-click on vocabulary to look it up in the dictionary.
Compare, generate, identify, recognize, represent, efficient, addition, subtraction, larger, smaller, greater than, less than, equal to, precision, patterns, tables
Technical Vocabulary: Right-click on vocabulary to look it up in the dictionary.
Place value, multi-digit, whole number, expanded form, hundredths, tenths, decimals, rules, standard algorithm, digit, equivalent forms, magnitude, rounding, fraction, denominator, numerator, number names, whole, unit
Technology:
- Base Blocks Decimals: http://nlvm.usu.edu/en/nav/frames_asid_264_g_2_t_1.html?from=search.html?qt=place+value (add and subtract decimal values; good visual, but not for core lessons, use as extension)
- Pan Balance — Numbers: http://illuminations.nctm.org/ActivityDetail.aspx?ID=26 (compare decimal numbers using pan balance)
- Concentration: http://illuminations.nctm.org/ActivityDetail.aspx?ID=73 (match fractions, decimals, multiplication, and more facts to equivalent representations)
- Coin Box: http://illuminations.nctm.org/ActivityDetail.aspx?ID=217 (coin value, counting coins, making change)
Common Misconception:
Students often treat decimals as whole numbers when comparing two decimals. They think the longer the number, the greater the value. For example, students think 0.03 is greater than 0.3.When reading decimals aloud, students should read the numbers as fractions, such as 3 hundredths or 3 tenths. If students read decimals this way, they visualize the fractional pieces the decimals represent. Discourage students from reading decimal numbers “point 03.”