This is one possible method for using the area model for division.

With this division strategy, students divide by breaking the dividend into its expanded form. Then, students use familiar multiplication facts to divide. It is suggested that this would be the first of three strategies for division (preceding partial quotients and the standard algorithm.

In this video, a student explains how to use the area model for multiplication. The area model is a multiplication strategy based on decomposing numbers basedon place value.

This video shows HOW and WHY we can shift decimals to make whole numbers when dividing.

Ratios

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Calculate with whole numbers up to 100 using all four operations.
Understand fraction notation and percents and translate among fractions, decimal numbers, and percents.
Interpret and use a number line.
Use tables to solve problems.
Use tape diagrams to solve problems.
Sketch and interpret graphs.
Write and interpret equations.

Lesson Flow

The first part of the unit begins with an exploration activity that focuses on a ratio as a way to compare the amount of egg and the amount of flour in a mixture. The context motivates a specific understanding of the use of, and need for, ratios as a way of making comparisons between quantities. Following this lesson, the usefulness of ratios in comparing quantities is developed in more detail, including a contrast to using subtraction to find differences. Students learn to interpret and express ratios as fractions, as decimal numbers, in a:b form, in words, and as data; they also learn to identify equivalent ratios.

The focus of the middle part of the unit is on the tools used to represent ratio relationships and on simplifying and comparing ratios. Students learn to use tape diagrams first, then double number lines, and finally ratio tables and graphs. As these tools are introduced, students use them in problem-solving contexts to solve ratio problems, including an investigation of glide ratios. Students are asked to make connections and distinctions among these forms of representation throughout these lessons. Students also choose a ratio project in this part of the unit (Lesson 8).

The third and last part of the unit covers understanding percents, including those greater than 100%.

Students have ample opportunities to check, deepen, and apply their understanding of ratios, including percents, with the selection of problems in the Gallery.

Students focus on interpreting, creating, and using ratio tables to solve problems.Key ConceptsA ratio table shows pairs of corresponding values, with an equivalent ratio between each pair. Ratio tables have both an additive and a multiplicative structure:Goals and Learning ObjectivesComplete ratio tables.Use ratio tables to solve problems.

This is one possible way to use the partial quotient strategy for division.

In this video, 5th grade students use the partial quotient division strategy to solve a 3-digit by 1-digit division problem. While this class begins with a brain dump, it is not necessary.

This resource is part of Tools4NCTeachers.

In this lesson students use the open number and various strategies to solve two-step story problems.

This resource is from Tools4NCTeachers. This file contains a set of 2 tasks (including scoring rubric and student recording sheet).  The tasks may be used for instruction or assessment. Remix this resource to include student work samples or addtional tasks.

This resource is from Tools4NCTeachers.In this lesson, students develop an understanding of place value by using arrow cards.  The focus of this lesson is on writing numbers using expanded form.Arrow cards are place value cards with an "arrow" or point on the right side.  Students can organize the cards to represent numbers in expanded notation. OR, they can overlap cards and (lining up the arrows) to form multi-digit numbers. Printable arrow cards are provided with this resource.. 

This resource is from Tools4NCTeachers.A Common Formative Assessment (CFA) provides a snapshot of current student understanding. It serves as a checkpoint, and may be used to guide future whole and small group instruction. This CFA addresses 2nd grade, Cluster 4 standards.

This resource is part of Tools4NCTeachers.

This purpose of this lesson is to give students the opportunity to problem solve and analyze other student solutions while working on adding two-digit numbers. This lesson assumes students have had previous experience with multiple addition strategies and that the class has posted strategy supports.

This resource is part of Tools4NCTeachers.

In this task, students count on from a given number, and analyze the place value of the digits within numbers. The task may be used for instructional or assessment purposes.

This resource is part of Tools4NCTeachers.

In this task, students group sets of counters into tens and leftover ones. The task may be used for instructional or assessment purposes.

This resource is part of Tools4NCTeachers.

In this lesson students use the open number and various strategies to solve two-step story problems.

This resource is part of Tools4NCTeachers.

In this lesson, students compare two-digit numbers based on the meanings of the tens and ones digits.

This resource is from Tools4NCTeachers.Students need distributed practice of newly-learned skills to develop fluency, build proficiency, and deepen understanding. This file contains directions for activities which may be used as Cluster 4 games or math stations.

This resource is part of Tools4NCTeachers.

In this lesson, students will compare and reason about the values of two-digit numbers based on the number of tens and ones in the numbers.

This resource is part of Tools4NCTeachers.

In this lesson, students build a two digit number using tens frames and then investigate strategies for determining how far the number is from 100. Students will write an equation to represent their thinking.

This resource is part of Tools4NCTeachers.

In this task, students apply their place value understanding to compose and decompose 2-digit numbers. A scoring rubric is included. The task may be used for instructional or assessment purposes.