### Standards & Objectives

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.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.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.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 0406.4.2
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 0406.2.8
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.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...

Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.

Essential and guiding questions:

Whole Group Questions

Write the key understandings that students should come to in the discussion of this task and questions you can ask in the whole group setting to support arrival at these key understandings.

The Model:

• How did you model the class?
• Did anyone do it differently?
• Are these solutions correct?
• Which model seems easier to use to you?

The Fractions:

• What is ¼ of 20? What is ½ of 20?
• How did you decide that these were the answers?
• Did anyone decide differently?
• Do both of these processes work?

The Context:

• What would happen if the class had 15 students in it?
• What is ¼ of 13? One‐half of 13?
• Can we have fractions of people?

Multiplying a Whole Number Times a Fraction:

• Can anyone see a relationship between the numbers ¼ and 20 that gives us a clue how to solve this without models?
• Do you think the relationship a×(b / c) = (a × b) / c always works?
• Can you give me another example of this in the problem?

Blooms taxonomy level:
Understanding
Extension suggestions:

Extensions:

If students can’t get started….

Assessing Questions

• Draw me a picture that represents a class of 22 students, any way you would like. Can you use that to model this problem?