Understand the place value system.
5.NBT
Number and Operations in Base Ten
Standards in this domain:
- 5.NBT.A.1
- 5.NBT.A.2
- 5.NBT.A.3
- 5.NBT.A.3a
- 5.NBT.A.3b
- 5.NBT.A.4
- 5.NBT.B.5
- 5.NBT.B.6
- 5.NBT.B.7
-
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 `sf (1/10)` of what it represents in the place to its left.
-
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.
-
5.NBT.A.3
Read, write, and compare decimals to thousandths.
-
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x `(1/10)` + 9 x `(1/100)` + 2 x `(1/1000)`.
5.NBT.A.3a is an embedded standard. This classification refers to problem-solving tasks where the underlying math concept in a Common Core standard is "embedded" within the problem, but the standard is not directly aligned to the problem. A student may use the underlying math concept in this standard to solve the task, but cannot be required to use that math concept due to the open-ended nature of problem solving. These tasks should not be given as an assessment, but rather used with students to practice a particular math concept or skill.
5.NBT.A.3a describes prerequisite understandings that are assessed at DOK3 in standard 5.NBT.A.3b. "Bamboo and the Botanist" is a good example of a task for which these understandings are required for its solution.
-
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
-
-
Perform operations with multi-digit whole numbers and with decimals to hundredths.
-
5.NBT.B.5 Standard not applicable.
Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.B.5 is not applicable. This classification refers to Common Core Standards that cannot be assessed through problem solving. For this reason, tasks have not been included for this particular standard.
5.NBT.B.5 is too narrowly defined to assess at DOK3.
Depth-of-Knowledge Level 3 (Strategic Thinking) requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. In most instances, requiring students to explain their thinking is a Level 3. Activities that require students to make conjectures are also at this level. The cognitive demands at Level 3 are complex and abstract. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning. An activity, however, that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3. Other Level 3 activities include drawing conclusions from observations; citing evidence and developing a logical argument for concepts; explaining phenomena in terms of concepts; and deciding which concepts to apply in order to solve a complex problem.
Depth-of-Knowledge definition per Normal L. Webb & others, Web Alignment Tool (WAT) Training Manual, University of Wisconsin-Madison and Wisconsin Center for Education Research, 2005, page 45. Accessed June 2012. http://wat.wceruw.org/index.aspx
-
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.
-
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.