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Lesson Study: A Handbook of Teacher-Led Instructional Change describes the basic steps of lesson study and provides practical resources

 

Lessons by Topic

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This index lists video lessons and lesson segments by mathematical topic and by the pedagogical features they illustrate. These include content topics (e.g., algebra, geometry, and statistics) and process topics (e.g., problem solving, representation, and proof). The same clip may illustrate several topics. The clips were chosen not for exemplary practices (such as the use of precise language) but to provide specific examples to provoke discussion of classroom practices. For more discussion of certain terms, see the Terminology section. Links provide access to further content on particular mathematical topics.

This list contains links to both mathematical and pedagogical topics, but the two are also listed as separate documents, one for mathematical topics and one for pedagogical topics.

Topics that refer to a lesson without a particular time clip are relevant throughout that lesson. Specific time clips are provided with topics when possible, but this list is not comprehensive.

Algebra,

  • distributive law, HK4, N3
  • equations, linear,
    • graphing, N1, S4, US1
    • identities, HK4
    • interpreting,
      • 0 = 0, HK4
      • 1 = 0, S4
    • solving, S4, HK4
    • system, HK2
  • equations, quadratic, S1
  • exponents, C1, C3, C4, US3, HK1 (degree 2 only)
  • expressions with variables, S2, US2
  • factoring, C2 3:28–4:20, N3, N4, S1
  • formulas, N1, C2
  • identity, HK4
  • inequalities, J3, J4
  • square (of a number), HK1
  • square root, HK1
  • variables, HK4, S2, US2

Angles, J1

Angle sum, A1, J1 6:50–8:00, HK3

Approximation, C2

Archimedes formula (C = 2r), C2

Area, of polygons, J2, HK3

Assessment, asking for show of hands, C1 19:29; C3 34:35; J2 22:47–22:58, 47:40–47:55, J3, J4

Auxiliary line, J1, US4

Blackboard, use of, to,

  • play a game, US2 49:10–53:00
  • present,
    • an idea, C2 5:40–6:03, J2 3:19–3:33
    • an example, HK3 1:13–1:18, 2:03–2:22, 3:04–3:25, 5:39–6:40, 14:00–14:51, 16:38–16:50, 19:20–19:46
    • a solution, HK1 1:30–1:34, 2:12–2:22, 2:31–2:44, 3:05–3:12, 7:00–8:00, 20:00–20:57; J2 19:45–21:07, 21:14–22:24, 42:14–46:00; J3 18:32–31:39; S2 14:22–23:06, 27:35–36:27, 36:27–42:40; S3 40:37–41:59
  • work a problem, C2 37:49–44:17; HK4 00:34–2:50, 24:21–27:46

Calculator use, A1 41:14–41:38; A3 15:01, 21:15, 34:31–41:00; A4 1:03:09; C1 4:48–5:45, 10:14–10:55, 12:03–12:59; C2 19:49–22:28, 26:44–27:46; S3 2:59 through remainder of lesson; US3 46:19

Circle, perimeter (circumference), C2

Congruence, A2

Connections,

  • made, C2 04:37–26:44, HK4 2:50–17:40, N1 6:11–11:50
  • possible (unmade), S2 15:03–16:44, 16:33–16:44, 17:07–19:39, 30:13–34:08; US1 1:49–2:21, 20:03–20:53, 40:40–41:15
  • real-world, N1 12:32–16:03, US2 20:54–26:47
  • with work in an earlier, grade, C2 10:37–11:32, 15:58; HK2 9:46–15:3; N2 7:03–10:28
  • lesson, N2 5:50–6:59

Counterexample, use of, HK4, 18:45

Different solution methods, see Problems with multiple entry points

Distributive law, HK4, N3

English as second language, HK1, HK3, HK4

Equations, linear,

  • graphing, N1, S4, US1
  • identities, HK4
  • interpreting,
    • 0 = 0, HK4
    • 1 = 0, S4
  • solving, S4, HK4
  • system, HK2

Equations, quadratic, S1

Exponents, C1, C3, C4, US3, HK1 (of degree 2 only)

Expressions with variables, S2, US2

Exterior angle, A1

Factoring, C2 3:28–4:20, N3, N4, S1

Formulas, N1, C2

Geometry,

  • angles, J1
  • angle sum, A1, J1 6:50–8:00, HK3
  • Archimedes formula (C = 2r), C2
  • area, polygons, J2, HK3
  • auxiliary line, J1, US4
  • circle,
    • perimeter (circumference), C2
  • congruence, A2
  • parallel lines, J1, J2
  • perimeter, C1, C2
  • polygons,
    • angle sum, A1, HK3
    • area, J2, HK3
    • convex, A1, HK3
    • non-convex, A1, HK3
    • perimeter, C1, C2
  • Pythagorean theorem (3),
    • applications of, C1, C2 8:34–9:58, C4 38:00–49:00, S3, US2 10:39–10:55
    • in three dimensions, C4 38:00–49:00, S3
    • introduction to, N2
    • preparation for, HK1
  • secants, US4
  • solids, S3
  • tangents, US4
  • triangles,
    • area, J2
    • congruence, A2

Geometry software, use of,

  • work in pairs, A1 19:06–42:15
  • whole class, J2 0:27–1:27, 46:36–49:47

Group work, S1 3:11–36:19; S2 20:00–23:02; US1 1:13–1:41, 2:54–3:25, 6:39–7:20, 11:37–13:12, 30:42–31:26

Heuristics,

  • auxiliary line, J1, US4, HK3
  • reducing to simpler problem, HK3, J1 4:32–10:10
  • reducing to previously solved problem, HK3
  • using related problems, C2 4:37–13:1

History of mathematics,

  • Archimedes, C2
  • Pythagoras, N2
  • van Ceulen, C2

Identity, HK4

Individual work, A1; J3 4:55–18:32; HK4 9:35–11:18, 27:46–31:42; N2 29:20–50:20; S4 8:18–17:03, 23:56–30:38, 34:46–37:53, 42:02–45:00

Inequalities, J3, J4

Instructional decisions,

  • choosing and using problems, J3; S1 25:16–35:30
  • introducing new topic with task involving old knowledge, HK4 00:34–2:58, 5:52–6:29
  • selecting students to present their work, J3 4:55–18:32; J4 9:10–16:08, 17:24–33:05, 34:44–46:00
  • problems for whole-class discussion, S4

Interactions with students, working

  • individually, N1 16:03–40:56; J3 4:55–18:32; S4 8:18–17:03, 23:56–30:38, 34:46–37:53, 42:02–45:00; US2 0:59–10:39
  • in groups, S3 9:45–11:02, 32:24–33:00; US1 1:13–1:41, 2:54–3:25, 6:39–7:20, 11:37–13:12, 30:42–31:26

Inverse of square root, HK1, N2, S3 36:30–49:00

Language (spoken and written),

  • English as second, HK1, HK3, HK4
  • modeling use of terms, HK4 17:14–17:27, 17:56, 27:34–27:46
  • precision, HK1 3:27–5:56; N1 34:20–36:09; US2, 37:30, 42:32; US3 7:45–9:56

Leading a discussion,

  • after an activity, A2 33:00–38:00; HK4 00:34–2:58, 5:52–6:29
  • summary of a solution, J4 24:54–33:05
  • synthesizing ideas, J4 49:47–50:30

Line graph, J3 1:25–5:01, 46:32; J4 27:27–29:01

Maintaining the challenge of the task, J3, N2, S3

Mathematics, preserving integrity of, while maintaining appropriate level, C2 14:58–18:47

Meaning of,

  • exterior angle, A1
  • identity, HK4
  • convex, A1 14:52–16:05, HK3 0:56–6:59
  • equilateral but not equiangular, HK3 6:40–21:35
  • non-convex, A1, HK3 5:39–6:40
  • polygon, A1 6:15–18:52
  • ray, A1
  • variable, HK4, US2

Mistakes in whole-class discussion, S2 20:00–23:02, S4 30:38–34:46

Motivating,

  • concept, HK4 1:00–19:27
  • formula, C2 0:00–26:44
  • different form of, C2 39:51
  • theorem, N2 5:50–6:59, 10:29–10:50
  • variables, usefulness of, J4

Multiple entry points (solution methods), problems with, J1

  • boundary problem, J3 1:00–31:39
  • cakes problem, J4

Multiple representations of a topic, J4 26:16–29:19, S4 37:45–41:58

Notation, use of, see Representations

Overhead projector,

  • homework, N1 01:25–12:32, US2 13:58–20:00
  • examples, US2 24:05–26:47, 26:47–30:17, 37:39–40:00
  • new material, US2 20:54–24:05
  • practice problems, US2 40:00–43:01
  • preparation for class activity, A1 6:15–19:08
  • Pythagorean theorem, informal proof of, N2 10:29–16:01

Parallel lines, J1, J2

Peer assessment, C3 34:47–38:54; S2 20:00–23:02

Perimeter, C1, C2

Polygons,

  • angle sum, A1, HK3
  • area, J2, HK3
  • convex, A1 14:52–16:07, HK3 0:56–6:59
  • equilateral but not equiangular, HK3 6:40–21:35
  • meaning of, A1 6:15–18:52
  • non-convex, A1 14:52–16:07, HK3 5:39–6:40

Presenting problems, J3 1:00–4:39

  • with no solution, HK1 25:02–25:13 , S4 38:57–41:45

Problem solving, J4

  • heuristics,
    • auxiliary line, J1, US4, HK3
    • reducing to simpler problem, HK3, J1 4:32–10:10
    • reducing to previously solved problem, HK3
    • using related problems, C2 4:37–13:1

Proof, N2, HK2, HK3, HK4

Pythagoras, N2

Pythagorean theorem,

  • applications of, C1, C2 8:34–9:58, C4 38:00–49:00, S3, US2 10:39–10:55
  • informal proof of, N2 10:29–16:01
  • in three dimensions, C4 38:00–49:00, S3
  • introduction to, N2
  • preparation for, HK1

Ray, A1

Real-world connections, N1 12:32–16:03, US2 20:54–26:47

Representations,

  • expanded and factored form, HK4 13:50–14:14
  • imprecise notation, HK4 26:33
  • notation for multiplying equation by constant, J4 00:00–7:00, S4 00:16–8:10
  • relationships among quantities,
    • bars, S2
    • line graph, J3 1:25–5:01, 46:32; J4 27:27–29:01
  • set notation used to indicate solution, S4 3:34

Scaffolding, N4, J1, US4

Secants, US4

Small group, US1 2:35–20:03, 20:52–30:35

Solids, S3

Solution launches the main topic of the lesson, HK4 3:17–4:33, 5:52–7:35, 12:47–17:40; J4 17:09–21:11, 23:30–25:43

Something "taught" but not learned,

  • taught N4 7:53–9:18
  • not learned N4 33:03–34:01

Square (of a number), HK1

Square root, HK1

  • inverse of, HK1, N2, S3 36:30–49:00

Statistics, A3, A4

Student-created problems, J1

Students, at the board,

  • play a game, US2 49:10–53:00
  • present,
    • ideas, C2 5:40–6:03, J2 3:19–3:33
    • examples, HK3 1:13–1:18, 2:03–2:22, 3:04–3:25, 5:39–6:40, 14:00–14:51, 16:38–16:50, 19:20–19:46
    • solutions, HK1 1:30–1:34, 2:12–2:22, 2:31–2:44, 3:05–3:12, 7:00–8:00, 20:00–20:57; J2 19:45–21:07, 21:14–22:24, 42:14–46:00; J3 18:32–31:39; S2 14:22–23:06, 27:35–36:27, 36:27–42:40; S3 40:37–41:59
  • work a problem, C2 37:49–44:17; HK4 00:34–2:50, 24:21–27:46

Students working in pairs, A1

Tangents, US4

Teacher responses to

  • unexpected student solutions, questions, misconceptions, A2 29:51–31:02; C2 3:21–4:07; J4 26:16–29:19, HK4 5:52–6:29
  • students struggling, J4 26:16–29:19, S4 16:54–23:49

Technology, use of,

  • calculator use, A1 41:14–41:38; A3 15:01, 21:15, 34:31–41:00; A4 1:03:09; C1 4:48–5:45, 10:14–10:55, 12:03–12:59; C2 19:49–22:28, 26:44–27:46; S3 2:59 through remainder of lesson; US3 46:19
  • geometry software,
    • work in pairs, A1, 19:06–4215
    • whole class, J2 0:27–1:27, 46:36–49:47
  • overhead projector,
    • homework, N1 01:25–12:32, US2 13:58–20:00
    • examples, US2 24:05–26:47, 26:47–30:17, 37:39–40:00
    • new material, US2 20:54–24:05
    • practice problems, US2 40:00–43:01
    • preparation for class activity, A1 6:15–19:08
    • Pythagorean theorem, informal proof of, N2 10:29–16:01
  • video, examples of linear and non-linear relationships, N1 12:32–14:36

Theorem, Motivating, N2

Triangles,

  • area, J2
  • congruence, A2

Van Ceulen, C2 20:07–22:10

Variables, HK4, S2, US2

Video, examples of linear and non-linear relationships, N1 12:32–14:36

Wait time, N1 3:30–12:15, S4 1:27, US1 2:00, 2:12, 7:27

Whole-class instruction,

  • students volunteer ideas, C2 04:37–26:44
  • teacher,
    • asks for show of hands, C3 34:35; J2 22:47–22:58, 47:40–47:55; J3; J4
      • calls on students for answers to,
        • homework, N1 1:25–12:32; US2 13:58–20:00
        • class work, HK4 11:18–12:31
    • describes solution method, S1 38:20–40:37
    • discusses problem, HK4 2:50–9:35, 12:31–17:40
    • presents problem, J3 1:00–4:39, S3 00:09–03:11
 
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