options: Solve systems of equations.

Interpret the structure of expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Work with equal groups of objects to gain foundations for multiplication.

Analyze patterns and relationships.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Use polynomial identities to solve problems.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Multiply and divide within 100.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Gain familiarity with factors and multiples.

Generate and analyze patterns.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Rewrite rational expressions.

Work with addition and subtraction equations.

Understand properties of multiplication and the relationship between multiplication and division.

Write and interpret numerical expressions.

Perform arithmetic operations on polynomials.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

Understand and apply properties of operations and the relationship between addition and subtraction.

Create equations that describe numbers or relationships

Add and subtract within 20.

Understand solving equations as a process of reasoning and explain the reasoning.

Represent and solve equations and inequalities graphically.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Task
Materials
Double sided counters
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Markers that are the same colors as the counters
Teacher-made “My Book of 5” (see below for detailed directions)
Action
Students will be given double sided counters/dots (see picture of counters, above). It is important for the markers to match the colors on the counters. Students take five counters in their cupped hands (or a cup), shake them around, pour them onto the desk. Next, they count how many counters are yellow and how many are red. Students then record the numbers in their book and write a corresponding equation. For example, if the counters landed so that 1 was yellow and 4 were red, then the student would draw one yellow dot and four red dots and then write “1+4=5” under the drawing. The student would then collect the counters and roll them again. For each combination of colors, the students record with a picture and an equation. Students continue until they fill their book of 5. The teacher can choose how many pages to put in, somewhere between five and eight is a good number so that students get a chance to see multiple combinations. After the students have completed their books, the teacher should have a whole-group discussion to make the number relationships explicit. One way to do this is to write each of the two addends into a table and to discuss possible patterns and reasons for the pattern. The teacher can ask specific questions such as, “What do you notice about the numbers in the table?” Or “Why is it that as one number gets bigger, the other number gets smaller?”
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Once students have completed the book, the activity can be repeated but with a book that has 6 pages. The students would then need to create one page for each possible way to make five. How to make "My Book of 5": The book could simply be blank pages stapled together and the student creates the circle and writes the equation under. If your students need more scaffolding each page of the book can consist of five empty circles which the students color in. This will make it impossible for the students to accidentally draw four or six circles. See below for an example: Empty Book Pages:
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Filled In by Student:
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Here is a photo of students working on different numbered books (not books of five):
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correct_option_index: 15