Content Standard(s):
Mathematics 8. Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given a variety of two-step word problems involving all four operations,
Apply understanding of operations to find solutions.
Use a model to represent the problem situation.
Write an equation to represent the problem using a symbol for the unknown quantity.
Explain and justify strategies and solutions.
Apply understanding of operations and estimation strategies including rounding to evaluate reasonableness of the solution. Teacher Vocabulary:
Unknown quantity
Mental computation
Estimation
Variable
Reasonableness
Rounding
Expression
Equation Knowledge:
Students know:
Characteristics of addition, subtraction, multiplication, and division.
Strategies for addition, subtraction, multiplication, and division.
Strategies for mental computation and estimating sums, differences, products, and quotients. Skills:
Students are able to:
Use a variety of strategies to solve two-step word problems involving all four operations. Write an equation to represent the problem context, and use a symbol for the unknown quantity. Justify strategy and solutions using mathematical vocabulary. Determine and justify reasonableness of solutions using mental computation strategies and estimation strategies. Understanding:
Students understand that:
Mathematical problems can be solved using a variety of strategies, models, and representations.
Contextual situations represented by multiplication and division. Reasonableness of solutions can be evaluated by using estimation strategies. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.3.8.1: Define the identity property of addition and multiplication.
M.3.8.2: Estimating sums and differences using multiple methods, including compatible numbers and rounding, to judge the reasonableness of an answer.
M.3.8.3: Apply commutative, associative, and identity properties for all operations to solve problems.
M.3.8.4: Identify a rule when given a pattern.
M.3.8.5: Solve addition and subtraction problems, including word problems, involving one-and two digit numbers with and without regrouping, using multiple strategies.
M 3.8.6: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
M.3.8.7: Represent multiplication and division with manipulatives.
M.3.8.8: Recall basic addition and subtraction facts.
Prior Knowledge Skills:
Explain addition and subtraction problems using concrete objects, pictures.
Use multiple strategies to add and subtract including counting on, counting back and using doubles.
Create a number pattern.
Use multiple strategies to add and subtract including counting on, counting back and using doubles.
Recall single-digit subtraction facts.
Recall single-digit addition facts.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 10. Identify the nearest 10 or 100 when rounding whole numbers, using place value understanding.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given two-digit or three-digit number to round to the nearest 10 or 100,
Identify the ten or hundreds that the number falls between. Plot the number on a number line between the tens or hundreds. Identify the nearest ten or hundred and justify the answer.
Identify a possible value of the unknown number when instructed that an unknown number will round to a given number when rounding to the nearest 10 or 100. Teacher Vocabulary:
Place value
Round
Nearest 10
Nearest 100
Benchmark number
Midpoint Knowledge:
Students know:
Values of the digits in the ones, tens, and hundreds places.
How to determine what is halfway between two multiples of 10 or 100.
Strategies for rounding to the nearest 10 or 100.
Use place value vocabulary and logical reasoning to justify solutions when rounding. Skills:
Students are able to:
Round whole numbers to the nearest 10 or 100.
Identify a possible value for a number which will result in a given number rounded to the nearest 10 or 100. Understanding:
Students understand that:
rounding is determining which ten or hundred a number is closer to. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.3.10.1: Define rounding.
M.3.10.2: Round whole numbers from 100 to 999 using whole numbers from 10 to 99.
M.3.10.3: Model rounding whole numbers to the nearest 100.
M.3.10.4: Round whole numbers from 10 to 99 using whole numbers from 1 to 9.
M.3.10.5: Model rounding whole numbers to the nearest 10.
M.3.10.6: Identify the steps in rounding two- and three-digit numbers. M.3.10.7: Round whole numbers from 1 to 9 and model to show proficiency.
M.3.10.8: Understand that the two digits of a two-digit number represent amounts of tens and ones.
M.3.10.9: Match the number in the ones, tens, and hundreds position to a pictorial representation or manipulative of the value.
Prior Knowledge Skills:
Determine the value of the number in the ones, tens and hundreds place.
Recognize the place value of ones, tens and hundreds.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 11. Use various strategies to add and subtract fluently within 1000.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given problems of addition and subtraction within 1000,
Fluently find sums and differences using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
Justify strategies and by relating the strategy to a written method and explain reasoning used.
Use estimation strategies to check for reasonableness and justify solutions.
Note: Standard algorithm for addition and subtraction is not a grade 3 expectation.
Teacher Vocabulary:
Fluently
Sum
Difference
Place value
Strategy Knowledge:
Students know:
The relationship between addition and subtraction operations.
How conceptual models support and give understanding to procedures for addition and subtraction. Skills:
Students are able to:
Use a variety of strategies to solve addition and subtraction problems within 1000. Understanding:
Students understand that:
Strategies for addition and subtraction will vary depending on the problem.
Strategies can include place value, properties of operations, and the relationship between addition and subtraction. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.3.11.1: Define the commutative and associative properties of addition and subtraction.
M.3.11.2: Subtract within 100 using strategies and algorithms based on the relationship between addition and subtraction.
M.3.11.3: Subtract within 100 using strategies and algorithms based on properties of operations.
M.3.11.4: Subtract within 100 using strategies and algorithms based on place value.
M.3.11.5: Add within 100 using strategies and algorithms based on the relationship between addition and subtraction.
M.3.11.6: Add within 100 using strategies and algorithms based on properties of operations.
M.3.11.7: Add within 100 using strategies and algorithms based on place value.
M.3.11.8: Recall basic addition and subtraction facts.
Prior Knowledge Skills:
Add within 100, including adding a two-digit number and a one-digit number and adding two two-digit numbers.
Add within 20, demonstrating fluency for addition within 10.
Add and subtract within 20.
Identify place value for ones, tens and hundreds.
Read number names one through one hundred.
Alabama Alternate Achievement Standards
AAS Standard:
