MTSD Draft Dated 9.5.13.mh

3.NF.1 Intervention Guide

Intervention Guide

3.NF.1

Develop understanding of fractions as numbers.

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b

About the Math: One meaning for a fraction is a number that represents a part of the whole. When a fraction is used to describe part of a region, the whole needs to be divided into equal parts. When dividing a region into equal parts, it is not necessary that the parts have the same shape as long as they have the same area. (Howard County Grade 3 Math Wiki 3.NF.1)

Consistent use of “unit fraction language” will help students make solid connections to this standard and the various models. For example, ¾ is “3 partitions of size ¼” or “3 equal shares of size ¼.” Folding fraction strips and modeling that language and supporting students as they practice is critical.

The Standards shown below develop the necessary skills for success with 3.NF.1. Students struggling in this standard may need an intervention that targets these previously taught skills. Links to supporting activities are found under each standard.

1.G.3 / 2.G.3 / 3.G.2
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Good tasks to address this standard:
/ Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Good tasks to address this standard:
/ Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Parts of a Square
Fractions with Color Tiles

Resources to support intervention work targeting 3.NF.1

Note: Reading Fractional Part of a Whole (Teaching Student-Centered Mathematics (2014). Van de Walle, et al.) (p. 211 - 220) will provide sound content knowledge for teachers intervening around this standard. Partitioning, iterating, fraction notation, fractions greater than one, and estimating with fractions are all discussed. Teaching tasks from this book are found in Resource #3.

**Prior to jumping into the instructional resources below make a fraction kit with your students. The lesson plan for this is found under the 3.NF.1 heading. Model, encourage, and support the use of “unit fraction language” as the strips are being folded.

Resource #1

Conceptua Fractions

Big Idea 1 Understanding Fractions

  • Topic 1 Model Part/Whole Relationships
  • Topic 2 Write Fractions

Big Idea 2 Understanding Mixed Numbers and Improper Fractions

  • Topic 1 Understand Mixed Numbers Order
  • Topic 2 Estimate Mixed Numbers

Before starting a group in Conceptua:

  • Paper/Pencil Tasks for Big Idea 1 are posted on MTSD RtIMath Website
  • You will need your teacher login for Conceptua Lessons
  • A “class” will need to be created for you in Conceptua. Email first and last names and grades of your students to Melissa.
  • Reserve your technology!

Resource #2

Conceptua Tool Library – Identifying Fractions

Use this tool to help students build conceptual understanding of fractions by linking visual models to numeric representations. Students learn about equal parts of a whole (denominators) and shaded parts (numerators).

Resource #3

Teaching Student-Centered Mathematics Grade 3-5 Vol II (Van de Walle, et al., 2014)

Fractional Parts of a Whole p. 211-220

Partitioning with Area Models

  • Activity 12.4 Correct Shares p. 212
  • Activity 12.5 How Far Did She Go? P. 212

Iterating

  • Activity 12.6 More, Less, or Equal to One Whole
  • Activity 12.17 Calculator Fraction Counting
  • The activities in Figure 12.10 and Figure 12.11 would provide solid teaching opportunities. Begin with unit fractions and move to proper fractions as student readiness indicates.

Resource #4

Ten-Minute Math Book

Fraction Cookie Game (p. 110-113)

You will need pattern blocks and Hexagon Cookie Sheet game board to play this game.

Resource #5

Fractions with Color Tiles

Resource #6

Naming the Whole for a Fraction – Illustrative Mathematics

Resource #7

Halves, Thirds, and Sixths – Illustrative Mathematics

Resource #8

Utah Education Network – Instruction Strategies and Assessment Tasks are very nice. They are found at the bottom of the pdf.

Resource #9

Fraction Tiles On-line Manipulative – build fractions from unit fractions. Nice small group lesson starter.

Resource #10

Fraction Concentration

Resource #11

Howard County “Assessing 3.NF.1” Provides 11 different assessment tasks that target 3.NF.1. Each task could be used as a teaching task.

Resource #12

Cuisenaire Fractions

Get Cuisenaire Rods from Melissa

Resource #13

Fraction Barrier Game – interactive game done with a partner. The first link are the directions, the second link is the game board.

Resource #14

Rational Number Project

Lesson 1 – This lesson offers a fairly comprehensive introduction to fractions that expands beyong 3.NF.1. Consistent use of “unit fraction language” will support meeting 3.NF.1.

***Substitute fraction strips for fraction circles.

Resource #15

Represent Fractions Concretely and Symbolically

For older students the teacher may wish to change the context of the lesson.

This next link offers a good review that might be appropriate for older students.

Resource #16

Match Me

A very basic introductory activity where students are matching symbols with pictorial representations of fractions.

Resource #17

4 practice problems that might serve as good first lesson to start conversations and get a feel for students’ initial understanding of 3.NF.1.

Resource #18

This is an on-line activity that allows you to compare fractions using a visual model, ONLY after you click on the Explain button. To stay in alignment with 3.NF.1 really push for the use of unit fraction language. This is best used as a teaching tool during small group intervention.

Resource #19

Single Fraction Finder

Students will practice dividing a whole into a fraction and visualize fractions on a number line.

Resource #20

Single Fraction Pointer

This activity was designed to help students better understand fractions by practicing dividing a whole into a fraction and visualizing fractions on a number line. This activity could be done independently.

Resource #21

Source: Utah Education Network

This PDF provides a very solid overview of 3.NF.1 with examples and understandings for the Concrete to Representational to Abstract Instructional Strategy. There 2 very nice story problems at the end of the document that can be used as teaching tasks.