Decimals

maiello0
Jan 17, 2018
3 min read

A true understanding of our place value system requires students to see the patterns within the value of digits in a number. Decimals help us see numbers that are in between the whole number values. Students need to have a lot of experience seeing, playing with and using blocks that represent those values to truly comprehend our base-10 system. This program allows them to use their knowledge to go deeper and explain how our algorithms work. Why do we line up decimals when adding and subtracting? Why don't we when multiplying? Why do we "move the decimal" when multiplying and dividing (spoiler: we don't!)? All of these questions will be answered.

2017-2018 School Year Goals:

- Grade 3 - intro to decimals, comparing/ordering, rounding, adding and subtracting, fraction equivalence

- Grade 4 - all of the above plus fraction equivalence, multiplying and dividing

- Grade 5 - multiplying and dividing using models.

2018-2019 and beyond goals:

- Grade 3 - intro to decimals, comparing/ordering, rounding, adding and subtracting

- Grade 4 - fraction equivalence, multiplying and dividing

Standards:

CCSS.MATH.CONTENT.4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. CCSS.MATH.CONTENT.4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. CCSS.MATH.CONTENT.4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Understand the place value system. CCSS.MATH.CONTENT.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. CCSS.MATH.CONTENT.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. CCSS.MATH.CONTENT.5.NBT.A.3 Read, write, and compare decimals to thousandths. CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). CCSS.MATH.CONTENT.5.NBT.A.3.B Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CCSS.MATH.CONTENT.5.NBT.A.4 Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths. CCSS.MATH.CONTENT.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. CCSS.MATH.CONTENT.5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.