All the activities in this lesson are addition and subtraction based. It is not designed to introduce addition and subtraction, rather, to supplement and enrich lessons already being taught. This lesson is not designed to be completed in one sitting. It may be done throughout an entire addition and subtraction unit. These activities may be used as starter activities when introducing new math concepts, particularly those that relate to addition and subtraction.

The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication.

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.

I use this activity to build understanding with equivalent fractions.Students model equivalent fractions with fraction bar models and number lines.  In both types of models students need to focus on partitioning or ceating equal parts.  They also need to make sure their models are properly labeled.Naming the multiplier or divisor allows students to practice with simplifying or unsimplifying fractions.

This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.

Estimated Lesson Time: 95 Minutes

Students will be able to:
-Understand how down payment, interest rate, term, loan type, and amortization table work together to impact overall mortgage payments
-Recognize the pros and cons of fixed- and adjustable-rate mortgages
-Determine whether a home equity loan or line of credit is a viable loan option
-Decide whether renting or buying makes the most sense

ANSWER KEY LINKS: Create a Next Gen Personal Finance (NGPF) account to access answer keys. They will be listed under the Full Year Curriculum tab.

This lesson is a re-engagement lesson designed for learners to revisit a problem-solving task they have already experienced. Students will activate prior knowledge of graphical representations through the 'what's my rule' number talk; compare and contrast two different learners' interpretations of the growing pattern; use multiple representations to demonstrate how one of these learners would represent the numeric pattern; make connections between the different representations to more critically compare the two interpretations. (5th/6th Grade Math)

Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and align paper-and-pencil calculations with the arrays. The lessons provide conceptual understanding of what occurs in a 2-digit multiplication problem. Partial product models serve as transitions to understanding the standard multiplication algorithm.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

When fractions are represented pictorially, they are always fractions ofsome whole. It is sometimes easy to forget to indicate this in a picture, particularly because the idea may be clear in our own mind. The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous. The teacher may wish to simply draw this picture on the board and have students think about what fraction the picture represents and follow this up with a discussion. When the whole is not specified for a fraction, a picture can represent an infinite number of different fractions: in this case there could be any number of small boxes (1,2,3, ...) in a whole and each possibility leads to a different meaning for the shaded or unshaded part of the picture.The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail. This particular task supports the demonstration of Mathematical Practice Standard 6, Attend to precision. Students are faced with elements of ambiguity in deciding what encompasses the whole. The whole in turn impacts the representation of a specific fraction. Students learn to appreciate, understand, and use mathematical vocabulary more precisely in interpreting and describing the whole and its fractional parts. While using different representations, such as pictures, they use appropriate labels to communicate the meaning of their representation (in this task the whole fraction and its accompanying fractional part).  Students also understand the possibility of different interpretations and therefore the necessity for precision in their work.

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

Students learn the connection between the counting sequence and experience from their daily lives in this daily activity. It also helps give students a sense of how "many" each number is.

This task acts as a bridge between understanding place value and using strategies based on place value for addition and subtraction.

In this ordering task each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number.

In this task students must place 4-digit numbers into order from smallest to greatest and greatest to smallest.

The purpose of this task is to extend students' understanding of fraction comparison.

In this task students compare numbers less than 100 to benchmark numbers and learn to build an understanding of the relative magnitude of numbers.

The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution.

The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.