In this unit of five lessons from Illuminations, learners begin with a number-line model and extend it to investigate linear relationships with the Distance, Speed, and Time Simulation from NCTM's E-Examples. Students then progress to plotting points and graphing linear functions while continually learning and reinforcing basic multiplication facts. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to download all student resources.

In this challenging instructional task students relate addition and subtraction problems to money and to situations and goals related to saving money.

This word problem may be used for instructional or assessment purposes, depending on where students are in their understanding of addition and how the teacher supports them.

In this math meets physics lesson, learners encounter the magical effect of reflection as they use a mirror to visually experience the concept of doubling quantities. This experience focuses learners' attention to using doubles as a strategy to make number operations easier, specifically addition. The book "Two of Everything" by Lily Toy Hong is used to introduce learners to these concepts. A game is used for discovery and practice and writing is used as closure to this lesson. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

The purpose of this task is for students to select 2 numbers from a set that sum to 5 (or any other number).

Students gain experience and practice with three types of word problems using the "Take From" context: result unknown, change unknown, and start unknown.

This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. However, students should not be discouraged from using individual counting to start if they are stuck. Often students will get tired of counting and devise the shortcut method themselves.

In this Illuminations lesson, students apply their knowledge of addition equations to investigate the equivalence of two numeric expressions using the "Pan Balance-Numbers" applet (cataloged separately). An instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given for the lesson as well as links to the applet and a student activity sheet(word format).

In this lesson plan students create graphs and analyze data based on the data provided by the United States Census Bureau. Students choose five states to focus on and create a bar graph for each, then students compare the data represented in the graphs and answer questions about the data. The lesson includes student activity sheet, the link to the U.S. Census Bureau is no longer active, please follow this link instead: http://www.census.gov/population/projections/files/stateproj/stpjpop.txt

In this math lesson, learners practice addition facts (with sums of 5, 6, 7, and 8) in a concentration-game format using dominoes. Then, learners generate sums of given numbers using a calculator, record the sums on a hundreds chart and look for patterns. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.

The four games that can be played with this applet help to develop counting and addition skills using frames of 10.

Thinking about numbers using frames of 10 can be a helpful way to learn basic number facts. The four games that can be played with this applet help to develop counting and addition skills. (This applet works well when used in conjunction with the Five Frame applet.)

This instructional task requires students to add four numbers to find the solution.

I created this lesson using the place value cards found on Helping With Math, https://www.helpingwithmath.com/printables/flashcards/2nbt3-number-cards01.htm and was used with a tier 3 fourth grade intervention math group to help students understand place value in expanded algorithms for addition. First I asked students to mentally add two three digit numbers that did not include zeros. When students added them by place value I notated it on a white board using expanded form and pointed out how it matched the student's mental strategy. I then gave students additional problems and students used the place value cards to expand the numbers and then wrote the corresponding expanded notation algorithm on whiteboards. Students had a little difficulty using the cards when zeros were in the tens and ones place. We addressed misconceptions with zeros in place values.

Students develop a physical understanding for the meaning of equality by trying to find equal lengths using rods.

This task helps students broaden and deepen their understanding of the equals sign and equality.

This lesson from Illuminations provides an introduction to the use of variables, and develops students' algebraic thinking. Students create variable machines to discover the value of words by assigning each letter of the alphabet a unique number value. Learning objectives, a materials list, a pdf file of the student worksheet, an instructional plan, questions for the students, assessment options, extensions, and teacher reflections are provided.

In this geometry lesson students classify triangles and explore side lengths of triangles to discover the Triangle Inequality Theorem. The resource includes an exploratory activity and student sheet (pdf), class discussion prompts, a small group spinner activity, extension suggestions, and links to two related resources (cataloged separately).

Big Ideas: Doubles facts can help determine numbers that can be divided equally. Even numbers create equal shares. This task builds on students' work with addition 'doubles' facts. In this lesson students will hear a story about how Ajani and Ian share everything equally. Students will determine whether they can share a given number of tokens to play arcade games. Students will group using manipulatives and learn what makes a number even or odd by splitting a number into two equal groups. Students will conceptually understand the patterns that even and odd numbers make. The mathematical concepts in this lesson build towards students' future work with building arrays, repeated addition, and multiplication.