ALEX Classroom Resources

ALEX Classroom Resources  
   View Standards     Standard(s): [MA2019] (5) 17 :
17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
[MA2019] (6) 2 :
2. Use unit rates to represent and describe ratio relationships.
[MA2019] (6) 3 :
3. Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.
[MA2019] REG-7 (7) 1 :
1. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.
[MA2019] REG-7 (7) 2 :
2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

c. Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate.
Subject: Mathematics (5 - 7)
Title: Super Bear: Comparing Mass
URL: https://aptv.pbslearningmedia.org/resource/mgbh-math-md-superbear/super-bear-comparing-mass/
Description:

Think about the relationships between the weight and size of similar objects. This interactive exercise focuses on using critical thinking skills and estimation skills to predict how many mini and regular gummy bears it takes to have the same mass as a super bear and then requires using data to complete calculations to see if your prediction was accurate.

This resource is part of the Math at the Core: Middle School collection.



   View Standards     Standard(s): [MA2019] (5) 9 :
9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result 2/51/23/7 by observing that 3/7 < 1/2.
[MA2019] (5) 11 :
11. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

a. Model and interpret a fraction as division of the numerator by the denominator (a/b= a ÷ b)

b. Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers
[MA2019] (5) 14 :
14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.
[MA2019] (5) 15 :
15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.
[MA2019] (5) 17 :
17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
[MA2019] (5) 19 :
19. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

a. Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

c. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.
[MA2019] (5) 20 :
20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.
Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 6, Topic E: Multi-Step Word Problems
URL: https://www.engageny.org/resource/grade-5-mathematics-module-6-topic-e-overview
Description:

Module 6, Topic E provides an opportunity for students to encounter complex, multi-step problems requiring the application of the concepts and skills mastered throughout the Grade 5 curriculum. Students use all four operations with both whole and fractional numbers in varied contexts. The problems in Topic E are designed to be non-routine problems that require students to persevere to solve them.  

While wrestling with complexity is an important part of Topic E, the true strength of this topic is derived from the time allocated for students to construct arguments and critique the reasoning of their classmates. After students have been given adequate time to ponder and solve the problems, two lessons are devoted to the sharing of approaches and solutions. Students partner to justify their conclusions, communicate them to others, and respond to the arguments of their peers.



   View Standards     Standard(s): [MA2015] (5) 5 :
5 ) 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-NBT2]

[MA2019] (5) 3 :
3. Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

a. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

b. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.
[MA2019] (5) 17 :
17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 1, Topic A: Multiplicative Patterns on the Place Value Chart
URL: https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-overview
Description:

Module 1, Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten systems. This exploration extends the place value work done with multi-digit whole numbers in Grade 4 to larger multi-digit whole numbers and decimals. Students use place value disks and a place value chart to build the place value chart from millions to thousandths. They compose and decompose units crossing the decimal with a view toward extending their knowledge of the 10 times as large and 1/10 as large relationships among whole number places to that of adjacent decimal places. This concrete experience is linked to the effects on the product when multiplying any number by a power of ten. For example, students notice that multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 10 10 as large (400.0) (5.NBT.2). Students explain these changes in value and shifts in position in terms of place value. Additionally, students learn a new and more efficient way to represent place value units using exponents (e.g., 1 thousand = 1,000 = 103) (5.NBT.2). Conversions among metric units such as kilometers, meters, and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A (5.MD.1).



   View Standards     Standard(s): [MA2019] (5) 6 :
6. Fluently multiply multi-digit whole numbers using the standard algorithm.
[MA2019] (5) 8 :
8. Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between addition/subtraction and multiplication/division; relate the strategy to a written method, and explain the reasoning used.

a. Use concrete models and drawings to solve problems with decimals to hundredths.

b. Solve problems in a real-world context with decimals to hundredths.
[MA2019] (5) 17 :
17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 2, Topic D: Measurement Word Problems with Whole Number and Decimal Multiplication
URL: https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-d-overview
Description:

In Module 2, Topic D, students explore multiplication as a method for expressing equivalent measures. For example, they multiply to convert between meters and centimeters or ounces and cups with measurements in whole number, fraction, and decimal form (5.MD.1). These conversions offer opportunities for students to not only apply their newfound knowledge of multi-digit multiplication of both whole and decimal numbers but to also reason deeply about the relationships between unit size and quantity (i.e., how the choice of one affects the other). Students are given the opportunity to review the multiplication of a whole number by a fraction, a skill taught in Grade 4.



   View Standards     Standard(s): [MA2015] (5) 5 :
5 ) 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-NBT2]

[MA2019] (5) 3 :
3. Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

a. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

b. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.
[MA2019] (5) 17 :
17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.
Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 1, Topic A: Multiplicative Patterns on the Place Value Chart
URL: https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-overview
Description:

Module 1, Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten systems. This exploration extends the place value work done with multi-digit whole numbers in Grade 4 to larger multi-digit whole numbers and decimals. Students use place value disks and a place value chart to build the place value chart from millions to thousandths. They compose and decompose units crossing the decimal with a view toward extending their knowledge of the 10 times as large and 1/10 as large relationships among whole number places to that of adjacent decimal places. This concrete experience is linked to the effects on the product when multiplying any number by a power of ten. For example, students notice that multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 10 10 as large (400.0) (5.NBT.2). Students explain these changes in value and shifts in position in terms of place value. Additionally, students learn a new and more efficient way to represent place value units using exponents (e.g., 1 thousand = 1,000 = 103) (5.NBT.2). Conversions among metric units such as kilometers, meters, and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A (5.MD.1).



ALEX Classroom Resources: 5

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