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Wrapping up the Unit

Number and Operations
Grace M. Burton
Location: unknown

In this final lesson of the unit, students display their knowledge of properties of objects for sorting and creating patterns. They also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations.

Place students in groups of up to four students, and provide each group with three number cubes, at least 64 counters, and a copy of the Collect the Counters Activity Sheet. Have each student pick a row, write his or her name next to it, and cover each number in that row with a counter. Then have the players take turns rolling the three number cubes, finding the sum of the numbers, and removing the counter from the sum. Allow the students to play a sample game as you circulate to be sure they understand how to play.

pdficonCollect the Counters Activity Sheet 

In this game, there are 16 possible sums that can result when three number cubes are tossed, namely 3‑18. Obviously, some of these sums are most likely than others. As students roll and attain various sums, they remove the counters from the game board. For instance, if a student had rolled four times and obtained sums of 7, 11, 13, and 17, their game board would look like this:

520 gameboard

You can adjust the rules for winning depending on how much time you would like students to spend playing this game. In the longest version, play until one student has removed all of the counters. (Note that the probability of rolling a 3 or an 18 is only 1/216, so it may take a while for these rolls to appear.) In shorter versions, play until a student removes 3, 4, or 5 counters in a row. (Asking students to identify the counters in a row that were removed by the winner can lead to a good discussion about probability and why some sums are more likely than others.)

Introduce the students to the Hungry Frog, which provides an opportunity for students to practice facts and develop fluency in recalling them. (When you click on "Click Here to Change Options," students may select from among the four binary operations—addition, subtraction, multiplication, division—and the game may include the use of negative numbers.)

Remind students to click on the frog whose lily pad has the accurate sum for the math fact that appears on the bug. Clicking on the frog makes it "hungry" and enables it to eat the bug with the correct fact. When a player clicks on a bug that has the accurate fact that matches the sum on the frog, he eats that bug and earns points for the player. The object of the game is to catch the correct bug before the bonus ball vanishes to win bonus points. [If students play in pairs or small groups, it may be necessary to specify a number of facts that constitute a turn for each player. This provides a more equitable distribution of play.] Have students document the beginning and ending bonus points and subtract the difference to determine the total number of points they collect in each turn.

To conclude the lesson, assign the students to play either the computer game or the number cube game.


Questions for Students 

1. What is the sum of 4 + 3? What other number pairs have the same sum?

[7; 0+7, 1+6, 2+5.]

2. What pair of numbers has a sum of nine? Are there any others with that sum?

[0+9, 1+8, 2+7, 3+6, 4+5.]

3. What do you know about 3 + 7 if you know the sum of 7 + 3? What property is this?

[The sum for both is 10; the commutative property.]

4. What numbers sum to three? To eleven? To five?

[0+3, 1+2; 0+11, 1+10, 2+9, 3+8, 4+7, 5+6; 0+5, 1+4, 2+3.]

Teacher Reflection 

  • Which students need more time to practice the addition facts? How will I provide this practice?
  • What other experiences will be helpful to the students who still have several facts to learn?
  • Which activities will foster individual remediation?
  • How will I ensure that the whole class has an opportunity for frequent practice with the addition facts?
  • What topics will I be teaching that require mastery of the addition facts?
  • What adjustments will I make the next time that I teach this lesson?
  • Which students have learned all the addition facts? What extension activities are appropriate for those students?
  • Did all the students display understanding of the addition properties [order property, additive identity, and the zero property]? What experiences do those who cannot use these properties need next?
  • Can the students explain how to find products on an addition chart?
  • Do the students recognize the facts they know and those they have yet to learn?
  • How can I help provide continued practice of the addition facts for students who are proficient with them?
  • What other learning experiences will help students explore addition as a natural part of daily activity?
  • How might I connect the fundamental ideas of this unit with lessons about related mathematics content?
  • What learning experiences would help the students not yet comfortable with these concepts to continue toward mastery of the addition facts?
  • What experiences would help the students extend their current level of understanding of this topic?
  • How will I provide brief, focused fact reviews throughout the year?
Number and Operations

Finding Addition Patterns

A game encourages students to find the sums of two one-digit numbers. Students explore commutativity and examine patterns on an addition table. They then use a personal addition chart to record and keep track of known facts.
Number and Operations

Finding Sums to Six

In this lesson, students discover the role of the additive identity and explore sums to six. They continue to complete their personal addition charts.
Number and Operations

Some Special Sums

Students practice doubles and doubles-plus-one addition facts. They record their current level of mastery of the addition facts on their personal addition charts.
Number and Operations

Addend Pairs to 12

Students practice their addition facts for sums up to 12 by playing a game. They add to their personal addition charts. Students are encouraged to practice the facts that they have not yet mastered. Finally, triangular flash cards help students practice addition facts.

Learning Objectives

Students will:

  • Practice the addition facts they have learned so far.
  • Identify the facts that they have left to learn.

NCTM Standards and Expectations

  • Understand the effects of adding and subtracting whole numbers.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.1
    Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.2
    Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.5
    Fluently add and subtract within 5.

-Kindergarten, Measurement & Data

  • CCSS.Math.Content.K.MD.B.3
    Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.3
    Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.4
    Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.C.6
    Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade 1, Number & Operations

  • CCSS.Math.Content.1.NBT.C.4
    Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade 1, Geometry

  • CCSS.Math.Content.1.G.A.1
    Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.

Grade 2, Algebraic Thinking

  • CCSS.Math.Content.2.OA.B.2
    Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.6
    Add up to four two-digit numbers using strategies based on place value and properties of operations.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.7
    Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.A.2
    Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP4
    Model with mathematics.