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Episodes: 53

Length: 15 to 30 min.

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Professional Development

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Mathematics and Technology

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Teaching Math: A Video Library, K-4

See how the National Council of Teachers of Mathematics standards are used in elementary classrooms across America. Elementary teachers tap the excitement and energy of children from kindergarten through grade 4 as they solve problems, learn to make connections between concepts, and communicate and reason mathematically. Teaching Math K-4 documents effective teaching and learning in many schools: small, large, rural, suburban and inner-city.

Episode Guide

1. Introduction — This overview shows the different parts of the library and their uses.

2. Ants Go Marching — Kindergartners develop number sense by exploring number concepts and number relationships. The number sequence is emphasized and the distinction is made between cardinal and ordinal meanings for number. NCTM standards: number sense and numeration, patterns and relationships, communication and connections.

3. Math Buddies — Kindergartners matched with sixth-grade coaches experience the numbers 1 through 50 through various activities involving hands-on experiences and common objects. NCTM standards: number sense and numeration, communication and connections.

4. Place-Value Centers — First-graders develop an understanding of the numeration system by relating counting, grouping and place-value concepts. Activities include measuring with Unifix cubes and using base-ten blocks. NCTM standards: number sense and numeration, measurement and connections.

5. Pumpkin Seeds — A grade 1-2 class, working in groups, develops their sense of larger numbers by estimating and counting the number of seeds in pumpkins. NCTM standards: number sense and numeration, estimation, communication and reasoning.

6. Animals in Yellowstone — Fourth- and fifth-graders develop number sense and meaning for large numbers by estimating how many bison, elk and pronghorn they saw on a field trip to Yellowstone National Park. Students debate and justify their estimates verbally and in writing. NCTM standards: number sense and numeration, estimation, problem solving and connections.

7. Cubes and Containers — Kindergartners sort Unifix cubes in various ways, focusing on the properties of the objects’ similarities and differences. By creating patterns, children develop an early understanding of geometry. NCTM standards: concepts of whole number operations, number sense and numeration, communication and reasoning.

8. Amazing Equations — Using the day of the month, first- and second-graders investigate the concepts of addition and subtraction as they share story problems that relate to the date. Teams use everyday language and experiences to connect to the mathematical language and symbolism for operations. NCTM standards: concepts of whole number operations, whole number computation, communication and connections.

9. Domino Math — First- and second-graders investigate number relationships and explore the concept of addition in a part-whole model using dominoes. They develop mathematical communication as they represent mathematical ideas with physical materials, words, diagrams and symbols. NCTM standards: concepts of whole number operations, whole number computation, problem solving and communication.

10. Marshmallows — Second-graders create and discuss a bar graph based on the number of marshmallows they estimate each person in their class would eat on a camping trip. After discussing their results, students determine how many bags of marshmallows to take. NCTM standards: concepts of whole number operations, statistics and probability, reasoning and problem solving.

11. What’s the Price? — Third-graders use problem-solving approaches—such as role playing or drawing pictures—to investigate and understand division. They make connections to everyday life and use calculators as they determine unit costs for two different boxes of cereal. NCTM Standards: concepts of whole number operation, fractions and decimals, problem solving and communication.

12. Dino Math — Kindergartners team up in buddy pairs to explore addition combinations using a “dinosaur math” mat. They work with basic addition facts and use a part-whole concept to perform the addition. NCTM standards: whole number computation, number sense, numeration and communication.

13. Windows Puzzle — First-graders investigate number combinations by working with a window puzzle (a square divided into four equal squares). In this task students explore both addition and subtraction employing physical materials to aid in computation as well as using mental math. NCTM standards: whole number computation, communication               and reasoning.

14. Wheel Problem — First-graders are asked how many vehicles could be in a parking lot if the total number of wheels is 24. Students review each step of the problem-solving process before they decide on which materials to use and develop strategies. NCTM standards: whole number computation, concepts of whole number operations, problem solving     and communication.

15. Bean Sprouts — Pairs of second-graders explore subtraction, based on the number of plants sprouting from the bean-seeds they have planted. The importance of context for student understanding and various approaches to problem-solving, are exemplified. NCTM Standards: concepts of whole number operations, reasoning, problem solving           and communication.

16. This Small House — Second- and third-graders use calculators, paper and pencil and mental math within a realistic task. Students plan the decorating of their milk carton houses using spatial sense to select appropriate furnishings while staying within their allocated budget. NCTM standards: whole number computation, geometry and spacial sense, connections and communication.

17. Choose a Method — A fourth-grade class shares their reasoning in evaluating the appropriateness of different computational methods (base-ten blocks, calculators, mental math, or paper and pencil) to specific problems. NCTM standards: whole number computation, estimation, communication and reasoning.

18. Thanksgiving Quilt — Creating quilt squares from construction paper, first graders develop spatial sense as they discuss and handle different shapes. They connect geometric ideas to number ideas as they cut squares into congruent triangles. NCTM standards: geometry and spacial sense, patterns and relationships, communication and connections.

19. Pattern Blocks — Second-graders learn the mathematical terms for pattern-block pieces: hexagon, trapezoid, square, triangle and rhombus. Ideas about fractions emerge as students spot size relationships between shapes. NCTM standards: geometry and spacial sense, number sense and numeration, reasoning and connections.

20. Shapes From Squares — A second/third-grade class develops spatial sense as they subdivide and change squares to create different shapes. The language of geometry—square, trapezoid, hexagon, etc.—grows naturally from their explorations. NCTM standards: geometry and spacial sense, communication and reasoning.

21. A Rocket Shape — Second- and third-graders experiment to subdivide a square to recreate a rocket shape. After completing their rockets, they reconvene as a class to discuss their difficulties and problem solving strategies. NCTM standards: geometry and spacial sense, measurement, problem solving and reasoning.

22. Circumference/Diameter — After reviewing the meaning of radius, diameter, center and circumference, fourth-graders working in teams measuring circular objects throughout the room. They are then challenged to find the relationship between the circumference and the diameter. NCTM standards: geometry and spatial sense, measurement, connections and reasoning.

23. Windows, Dinos and Ants — First-graders are engaged in problem solving and measuring with both standard and nonstandard units. Students work in groups to measure three different distances: ant farm tunnels, dinosaurs and the length from their classroom window to the playground below. NCTM standards: measurement, number sense and numeration, problem solving and reasoning.

24. How Long is a Minute? — Having already studied the concept of an hour, first-graders investigate time as a measure of duration. They list activities, such as writing their name, that could be accomplished within a minute, then estimate how many times in one minute they could do it. NCTM standards: measurement, estimation, reasoning and connections.

25. Balloon Travel — In an integrated math/science lesson, second- and third-graders collect data to answer questions such as, “What is the farthest a balloon can travel before falling?” To answer the question, they must understand distance, volume, capacity and time. NCTM standards: measurement, estimation, connection and problem solving.

26. Meter Cords — Third- and fourth-graders use linear measurement in learning about decimals. Students measure different items with a meter divided into 10 parts then learn to write their measurements using decimal notation. NCTM standards: measurement, fractions and decimals, connections and communications.

27. Pencil Box Staining — Fourth-graders are faced with the task of finding out how much stain to buy from the hardware store and encounter problems as they work with many mathematical ideas in the context of a real application. Students work in groups with pencil box pieces, a ruler, calculator and instruction sheet. NCTM standards: measurement, fractions and decimals, problem solving and reasoning.

28. Ladybugs — First-graders choose ladybugs as a topic for learning. Based on their observations, students make bar graphs and a class chart to record the number of heads, wings, feet and antennas ladybugs have. They make connections among real objects, diagrams and numerals. NCTM standards: statistics and probability, number sense and numeration, connections and communication.

29. Woodpecker Habitat — First- and second-graders apply probability and sampling techniques to their study of the habitat of the endangered red-cockaded woodpecker. Using colored cubes to represent elements in the environment, students simulate factors that might harm or help the birds. NCTM standards: statistics and probability, whole number computation, reasoning and connections.

30. Bubble Gum Contest — Third-graders stage a bubble gum blowing contest using sampling to determine the ratio of winners to entrants. They enlarge their sample, collecting data from all the third-graders in their school and use fractions to interpret the data. NCTM standards: statistics and probability, fractions and decimals, connections and communication.

31. Dice Toss — Fourth-graders work with statistics, probability, fractions and decimals while conducting an experiment to see which sum comes up most often when rolling two dice. Once the groups complete their experiments, they compile their findings on a class bar graph and analyze the graph. NCTM standards: statistics and probability, fractions and decimals, communication and reasoning.

32. Questioning Data — A fourth- through sixth-grade class takes data collected from surveys on questions of personal interest. They then represent the data in a graph, and write about what the graph interprets and the questions they still have about the survey subject. NCTM standards: statistics and probability, connections, communication           and reasoning.

33. Fraction Strips — First- and second-graders make fraction pieces from paper strips and play a game that involves covering a whole strip with fractional pieces. As they play they informally add fractions and make connections from objects and actions to symbols. NCTM standards: fractions and decimals, number sense and numeration, reasoning          and communication.

34. Arrays and Fractions — A first- through third-grade class investigates fractional parts of a set by building arrays that represent wholes of different sizes. In their task they use mathematical language and symbols and form mathematical connections among concepts of addition, area, multiplications, division and fractions. NCTM standards: fractions and decimals, number sense and numeration, reasoning and communication.

35. Everyday Decimals — Second- and third-graders extend their understanding of common fractions to notation for decimal fractions and to the numeration system. They interpret the use of decimals in the real world by bringing to class items that have decimals or fractions written on them. NCTM standards: fractions and decimals, number sense and numeration and connections.

36. Cookies to Share — Through a story about sharing cookies, fourth-graders investigate a the problem of dividing eight cookies among 12 children. It helps them develop meaning for the concept of division and leads to the use of fractions. NCTM standards: fractions and decimals, number sense and numeration, communication and connections.

37. Fractions and Geoboards — Fourth- and fifth-graders investigate the concept of halves using the geoboard as an area model. They learn that one-half means two equal-sized parts with equal areas, but that are not necessarily congurent. NCTM standards: fractions and decimals, geometry and spacial sense, reasoning and problem solving.

38. People Patterns — One of several lessons on patterns, individual kindergartners are lined up to represent different patterns to the class. In groups they create their own patterns from simple two-element patterns or more complex six-element patterns to share with the class. NCTM Standards: patterns and relationships, number sense and numeration, communication and reasoning.

39. All Sorts of Buttons — Kindergartners and first-graders hear a story about buttons, then sort their own collection of buttons to develop skills of classification—observing likenesses and differences. Students see that objects can be looked at in a number of ways and develop a sense of pattern and regularity. NCTM standards: patterns and relationships, number sense and numeration, reasoning and connections.

40. Story-Based Centers — Second-graders work at learning centers around their classroom that are based on the story “Caps for Sale.” At the centers students construct graphs, figure out coin combinations to equal 50 cents, use a computer to explore patterns and write story problems and number sentences. NCTM standards: patterns and relationships, whole number computation, connections and communications.

41. Products and Sums — Exploring relationships between addition and multiplication, fourth-graders represent numbers, sums and products with symbols and with geometric patterns on paper. NCTM standards: patterns and relationships, number sense and numeration, reasoning                   and communication.

42. Valentine Exchange — A bilingual fourth-grade class uses a Valentine’s Day card exchange problem to explore mathematical relationships and share problem solving strategies. NCTM standards: patterns and relationships, number sense and numeration, problem solving and reasoning.

43. Beans, Beans, Beans — Kindergartners sharpen their estimation skills and number sense as part of a unit on plants and seeds. Using three known quantities for reference, student groups must estimate the number of an unknown quantity of beans, and then count the beans by tens. NCTM standards: estimation, number sense and numeration, reasoning and communication.

44. How Many People WIll Fit? — First-graders investigate the concept of area by figuring out how many people will fit in four different areas in the school building. They organize and record solutions and use measuring, counting and addition to find the total number of people. NCTM standards: estimation, measurement, reasoning and problem solving.

45. Cranberry Estimation — Second-graders in Massachusetts estimate the number of scoops of cranberries that will fit in a jar. They report, graph and discuss group estimates with the class as the concepts of range, mode and median emerge. NCTM standards: estimation, statistics and probability, reasoning and connections.

46. Buffalo Estimation — A third-grade class that has been studying the Oregon Trail explores estimation by figuring out how many buffalo would fit in their classroom and on their playground. Students develop number sense as they think about the reasonableness of estimates and use a referent to adjust their estimates. NCTM standards: estimation, number sense and numeration, reasoning and connections.

47. The White Pages — This lesson helps fourth-graders develop number sense by exploring magnitudes of large numbers (the number of listings in the phone book) and reasonableness of estimates. Students mark their estimates on a number line and justify their estimates verbally and in writing. NCTM standards: estimation, number sense and numeration, problem solving and connections.

48. Problem Solving — The half-hour program includes 13 classroom excerpts from the content standards lessons which illustrate students investigating and learning mathematics through problem solving. Teachers share their approaches and observations.

49. Communication — The half-hour program includes 18 classroom excerpts from the content standards lessons which show students representing, discussing, reading, writing and listening as vital parts of learning and using mathematics. It shows how communication fosters an understanding of mathematical ideas and the language of mathematics.

50. Reasoning — The half-hour program includes 16 classroom excerpts from the content standards lessons which illustrate the central role of reasoning in mathematics. As students explain and justify their thinking and solutions throughout the excerpts, teachers emphasize that how a problem is solved is as important as its answer.

51. Mathematical Connections — The half-hour program includes more than a dozen classroom excerpts from the content standards lessons that illustrate mathematical connections. Connections are made among different topics in mathematics, to other curriculum areas and to students’ daily lives.

52. Classrooms Over Time — Problem solvers fall and spring.

53. Classrooms Over Time: Long Term Projects — Two segments about Steven Levy’s class at the Bowman School, Lexington, MA. Segment 1 – Pencil Box Staining Segment 2 – Bike Path Usage.

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