4th Grade Task: Closer to 1

4th Grade Task: Closer to 1

Standards & Objectives

Academic standards
CCSS.Math.Content.4.MD.A.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single...
CCSS.Math.Content.4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including...
CCSS.Math.Content.4.MD.B.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of...
CCSS.Math.Content.4.NBT.A.2
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on...
CCSS.Math.Content.4.NBT.A.3
Use place value understanding to round multi-digit whole numbers to any place.
CCSS.Math.Content.4.NBT.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place...
CCSS.Math.Content.4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the...
CCSS.Math.Content.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size...
CCSS.Math.Content.4.NF.A.2
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to...
CCSS.Math.Content.4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
CCSS.Math.Content.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
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...
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...
CCSS.Math.Content.4.OA.A.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many...
CCSS.Math.Content.4.OA.A.2
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown...
CCSS.Math.Content.4.OA.A.3
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which...
GLE 0406.1.2
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
GLE 0406.2.2
Develop fluency with multiplication and single-digit division.
GLE 0406.2.5
Add and subtract fractions with like and unlike denominators.
GLE 0406.2.6
Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations.
GLE 0406.3.1
Extend understanding of a variable to equations involving whole numbers, fractions, decimals, and/or mixed numbers.
GLE 0406.3.3
Translate between different forms of representations of whole number relationships.
GLE 0406.4.2
Understand and use measures of length, area, capacity, and weight.
GLE 0406.4.3
Solve problems that involve estimating and measuring length, area, capacity and weight.
GLE 0406.5.1
Collect, record, arrange, present, and interpret data using tables and various representations.
SPI 0406.2.10
Solve contextual problems using whole numbers, fractions, and decimals.
SPI 0406.2.11
Solve problems using whole number multi-digit multiplication.
SPI 0406.2.5
Generate equivalent forms of common fractions and decimals and use them to compare size.
SPI 0406.2.8
Add and subtract proper fractions with like and unlike denominators and simplify the answer.
SPI 0406.3.1
Use letters and symbols to represent an unknown quantity and write a simple mathematical expression
SPI 0406.4.7
Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight.
SPI 0406.5.1
Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs).
SPI 0406.5.2
Solve problems using estimation and comparison within a single set of data.
TSS.Math.4.MD.A.2
Solve one- or two-step real-world problems involving whole number measurements with all four operations within a single system of measurement including...
TSS.Math.4.MD.B.4
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems...
TSS.Math.4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 + 1/5 + 1/5 + 1/5.
TSS.Math.4.NF.B.4
Apply and extend previous understandings of multiplication as repeated addition to multiply a whole number by a fraction.
TSS.Math.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...
TSS.Math.4.OA.A.2
Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguish multiplicative comparison from additive comparison.
TSS.Math.4.OA.A.3
Solve multi-step contextual problems posed with whole numbers and having whole-number answers using the four operations, including problems in which...
 
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Activity/Task Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

If students can’t get started….

Assessing Questions:

  • Which is smaller: ¾ or 4/3? How do you know?

Advancing Questions:

  • How does ¾ compare to 1 – is it greater or less than 1? How do you know?
  • How does 4/3 compare to 1 – is it greater or less than 1? How do you know?
  • Which pieces are smaller – fourths or thirds?

If students finish early….

Assessing Questions:

  • How do you know that you have shown that for all fraction pairs, the one less than 1 is closer to 1?

Advancing Questions:

  • Do you think this will be true of other type of fraction pairs, like 5/7 and 7/5? Why or why not?

Whole Group Questions:

Part A:

  • Who can explain how you decided where to place these two fractions on the number line? Did anyone change his/her placement after working part B? Why? What made you change your mind?

Part B:

  • How did you decide which is closer to 1? What did you consider? 
  • By comparing only the denominators, what does that tell us? How do the size of the pieces compare? What does the numerator tell us?
  • How many ¼’s do we have? How can this be expressed by repeated addition? Multiplication?
  • How may 1/3’s do we have? How can this be expressed by repeated addition? Multiplication?
  • How does this help us decide?

Part C:

  • Do we think that what happened in part B will happen for all special fraction pairs? How could we tell? Who can share his/her thinking? What are some important things to consider in order for us to give an argument?