This document provides an overview of scaffolding instruction for addition and subtraction. It discusses using graphic organizers and manipulatives to build conceptual understanding from concrete to abstract levels. Specific lessons are outlined for pre-kindergarten through second grade that model addition and subtraction using objects, pictures, and number sentences. Representational tools like linking cubes, part-part-whole mats, and base ten blocks are employed to scaffold learning.

1. Addition and Subtraction Scaffolding Instruction

3. TEKS Focus Use organizers to build understanding of addition and subtraction of two-digit numbers. Use organizers to bridge the development of addition and subtraction to the abstract of writing number sentences. Use story mats and manipulatives to develop joining and separating up to 20 objects. (2.3) The student adds and subtracts whole numbers to solve problems (2.3B) The student is expected to model addition and subtraction of two-digit numbers with objects, pictures, words, and numbers. (1.3) The student recognizes and solves problems in addition and subtraction (1.3A) The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. (K.4) The student models addition (joining) and subtraction) separating (K.4) The student is expected to model and create addition and subtraction problems in real situations with concrete objects. Modeling Addition and Subtraction Modeling Addition and Subtraction Modeling Addition and Subtraction Second Grade First Grade Kindergarten

4. TEKS Focus Use organizers and games to select and solve addition and subtraction situations. Use organizers to develop, bridge, and build basic addition and subtraction facts. (2.3) The student adds and subtracts whole numbers to solve problems (2.3) (C) select addition or subtraction to solve problems using two-digit numbers, whether or not regrouping is necessary (2.3) The student adds and subtracts whole numbers to solve problems (2.3) (A) recall and apply basic addition and subtraction facts (to 18) (1.3) The student recognizes and solves problems in addition and subtraction (1.3) (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18 – 9 = 9) Selecting Addition or Subtraction to Solve Problems Basic Addition and Subtraction Facts Basic Addition and Subtraction Facts Second Grade Second Grade First Grade

5. Scaffolding Instructional Focus: Scaffolding

9. Reading Academies

11. What is Scaffolding in Mathematics Instruction? What Is Scaffolding in Mathematics Instruction?

14. Scaffolding Instruction Through Questioning “ Teachers can use questions as a kind of scaffolding to help students reach higher levels of thinking and learning. . . In the asking of questions, teachers are thinking actively and helping students be active thinkers” (Walsh and Sattes, 2005, p 23).

16. Pre Kindergarten and Kindergarten Lesson Modeling Addition and Subtraction

17. 1 st Series of Lessons: Modeling Addition & Subtraction (3.3) The student is expected to model addition and subtraction using pictures, words, and numbers. (2.3B) The student is expected to model addition and subtraction of two-digit numbers with objects, pictures, words, and numbers. (1.3A) The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. (K.4) The student is expected to model and create addition and subtraction problems in real situations with concrete objects. PK Guidelines Combines separates and names “how many” concrete objects. (3.3) The student adds and subtracts to solve meaningful problems involving whole numbers. (2.3) The student adds and subtracts whole numbers to solve problems. (1.3) The student recognizes and solves problems in addition and subtraction. (K.4) The student models addition (joining) and subtraction) separating. PK Guidelines Number and Operation

18. Create a shell story. Trace the shells to retell at home. Extend Students choose beach mat or zoo mat and are given 3 scenarios to solve with manipulatives ; students will create a scenario. Evaluate Students will again experience joining and separating of sets with a beach mat and sea shells. Elaborate 2 Students will create their own animal cards and add to the story using blank cards. Elaborate 1 Reread the story with students acting it out physically and with manipulatives of a zoo mat and animal cards pointing out separating, joining, and relating to the size of the group ( zoo mat and linking cubes are also available). Explore & Explain There are questions eliciting prior knowledge about experiences going to zoos and being in plays. Read the story. Engage Model Addition & Subtraction for PK-K

19. One Gorilla

30. Time to Reflect Which manipulative is easier to use and to understand the concepts for this activity?

31. Part-Part-Whole Mat for Addition Explore

33. Part-Part-Whole Mat 10 IIII IIII

36. Five monkeys scream and shout. It doesn’t take long for them to get out! 10 5 + = 15

39. Cling! Clang! It’s dinner time! Five monkeys swing home in rhyme. 15 5 - = 10

47. Elaborate 2

48. Time to Reflect How did we use visuals to move the students from the concrete to the abstract level of learning?

50. Create a shell story. Trace the shells to retell at home. Extend Students choose beach mat or zoo mat and are given 3 scenarios to solve with manipulatives ; students will create a scenario. Evaluate Students will again experience joining and separating of sets with a beach mat and sea shells. Elaborate 2 Students will create their own animal cards and add to the story using blank cards. Elaborate 1 Reread the story with students acting it out physically and using manipulatives of a zoo mat and animal cards pointing out separating, joining, and the relationship to the size of the group ( zoo mat and linking cubes are also available). Explore & Explain There are questions eliciting prior knowledge about experiences with zoos and being in plays. Read the story. Engage Model Addition & Subtraction for PK-K

51. First Grade Lesson Modeling Addition and Subtraction

52. 1st Series of Lessons: Modeling Addition & Subtraction (3.3) The student is expected to model addition and subtraction using pictures, words, and numbers. (2.3B) The student is expected to model addition and subtraction of two-digit numbers with objects, pictures, words, and numbers. (1.3A) The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. (K.4) The student is expected to model and create addition and subtraction problems in real situations with concrete objects. PK Guidelines Combines separates and names “how many” concrete objects. (3.3) The student adds and subtracts to solve meaningful problems involving whole numbers. (2.3) The student adds and subtracts whole numbers to solve problems. (1.3) The student recognizes and solves problems in addition and subtraction. (K.4) The student models addition (joining) and subtraction) separating. PK Guidelines Number and Operation

53. Uses the Linking Cubes on a String and accompanying recording sheets. Optional Tool There is a pizza game with ten frames or five frames. Extend The students will create and write a new scenario , then give the story to a partner and let the partner write the number sentence. Evaluate Students will embellish the zoo story by drawing the new story and writing the matching number sentence. Elaborate Finish the story and experience using the part/part whole mat with the subtraction portion of the story. Explain 2 Subtraction will be modeled with the visual of the part/part whole mat and zoo mat with the poem. Explore 2 Read the story and experience using the part/part whole mat with the addition portion of the story. Explain 1 Addition will be modeled with the visual of the part/part whole mat and zoo mat with the poem. Explore 1 There are questions eliciting prior knowledge about experiences with zoos and being in plays. Read the story while students physically act it out with manipulatives. Engage Model Addition & Subtraction for Grade 1

54. Linking Cubes on a String Engage Optional Tool

55. Recording Sheet for Linking Cubes on a String Up to 15 Optional Recording Sheet 6 + 4 = 10

56. Recording Sheet for Linking Cubes on a String Up to 20 6 + 4 = 10 Optional Recording Sheet

58. Second Grade Lesson Modeling Addition and Subtraction

59. Progression of Knowledge and Skill Statements (3.3) The student is expected to model addition and subtraction using pictures, words, and numbers. (2.3B) The student is expected to model addition and subtraction of two-digit numbers with objects, pictures, words, and numbers. (1.3A) The student is expected to model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences. (K.4) The student is expected to model and create addition and subtraction problems in real situations with concrete objects. PK Guidelines Number and Operations (3.3) The student adds and subtracts to solve meaningful problems involving whole numbers. (2.3) The student adds and subtracts whole numbers to solve problems. (1.3) The student recognizes and solves problems in addition and subtraction. (K.4) The student models addition (joining) and subtraction) separating. PK Guidelines Number and Operations

60. Show transparencies of questions for students to solve . Evaluate Partners will compare their two pinecones and formulate questions and answers. Elaborate Students share and explain how they found the number of scales on their pinecone and explain how to use linking cubes or a base ten organizer. Explain Students will discuss the strategies for finding the amount of scales on a pinecone and explore how to use a base ten or linking cubes organizer. Explore Estimate the scales on a pinecone. Engage Model Addition & Subtraction for Grades 2-3

61. 9 8 7 6 5 4 3 2 1 Units Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10

62. Linking Cube Organizer 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate + Ones Tens Hundred

63. 15 + 23 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate + 5 1 Ones Tens Hundred

64. 15 + 23 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate 3 8 3 2 + 5 1 Ones Tens Hundred

65. 15 + 23 Describe the Results in Words and Numbers 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate = 38 3 tens and 8 ones 30 + 8 38

66. 24 + 36 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate + 4 2 Ones Tens Hundred

67. 24 + 36 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate 0 1 6 6 3 + 4 2 Ones Tens Hundred

68. 24 + 36 Describe Results in Words and Numbers 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate 6 tens and 0 ones 60 + 0 60

69. 24 + 38 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate 2 1 6 8 3 + 4 2 Ones Tens Hundred

70. 24 + 38 Describe Results in Words and Numbers 9 8 7 6 5 4 3 2 1 Ones Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 Elaborate 6 tens and 2 ones 60 + 2 62

72. Base Ten Blocks Organizer Ones 9 8 7 6 5 4 3 2 1 Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 67 + 45 Explain

73. Base Ten Blocks Organizer Ones 9 8 7 6 5 4 3 2 1 Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 67 + 45 Explain

74. Base Ten Blocks Organizer Ones 9 8 7 6 5 4 3 2 1 Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 67 + 45 Explain

75. Describe the Results in Words and Numbers Ones 9 8 7 6 5 4 3 2 1 Tens 10 9 8 7 6 5 4 3 2 1 100 90 80 70 60 50 40 30 20 10 1 hundred 1 ten 2 ones 100 + 10 + 2 67 + 45 = 112

79. First and Second Grade Lesson Basic Addition and Subtraction Facts

80. TEKS Focus Use organizers and games to select and solve addition and subtraction situations. Use organizers to develop, bridge and build basic addition and subtraction facts. (2.3) The student adds and subtracts whole numbers to solve problems (2.3) (C) select addition or subtraction to solve problems using two-digit numbers, whether or not regrouping is necessary (2.3) The student adds and subtracts whole numbers to solve problems (2.3) (A) recall and apply basic addition and subtraction facts (to 18) (1.3) The student recognizes and solves problems in addition and subtraction (1.3) (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18 – 9 = 9) Selecting Addition or Subtraction to Solve Problems Basic Addition and Subtraction Facts Basic Addition and Subtraction Facts Second Grade Second Grade First Grade

81. Play 3 in a row! with cards which have the quantity of the numerals in pictorial form or numerical form. Evaluate Have students solve + =13 using a variety of manipulatives and organizers. Elaborate Students will identify all possible strategies to solve five facts. Explain Discuss various strategies and share with the students the make ten mat, doubles and near doubles mat, and part/part whole mat used for related facts, and splitting strategies, compensation. Explore Solve a problem 9 + 8. Engage Basic Facts for Addition & Subtraction for Grades 1-2

83. Doubles and Near Doubles

84. Doubles 5 + 5 = 10 6 + 6 = 7 + 7 = 12 14

86. Doubles and Near Doubles: 5 + 5 = 10 6 + 6 = 7 + 7 = 12 14 5 + 6 = 6 + 7 = 11 13 Explore thinking strategies like these or realizing that 7 + 8 is the same as 7+7+1 will help students see the meaning of the operations. Such explorations also help teachers learn what students are thinking. NCTM

89. 6 + 8 = How can the students use the Make Ten Strategy to solve this problem?

90. 6 + 8 =

91. 6 + 8 =

92. 6 + 8 =

97. Reflect: What modes of learning were used to help students learn their basic facts? Fill the reflection sheet.

98. Second and Third Grade Lesson Selecting Addition or Subtraction to Solve Problems

99. Give the students several manipulatives and a variety of organizers to use when solving problems. Evaluate Play Race to Win! solving the problem. Elaborate 2 Play Race to Win! giving only the number sentence. Elaborate 1 Have the students solve a problem using a problem solving organizer. Explain Give a problem and demonstrate the on the problem solving mat. Explore/ Explain Play 99 with organizers. How can you play 99 with the least amount of rolls? Engage Select Addition & Subtraction for Problem Solving for Grades 2-3

100. Reflect: Look at your scaffolding handout and highlight a scaffolding technique you would like to start using immediately.