Number Grid Puzzles
Amy Cattabriga
Number Grid Puzzles /A 1st Grade Math Lesson /
Amy Cattabriga /
University of New England
EDU-723
I modified this lesson from the first grade Everyday Math curriculum. The original lesson, which only involved discussing the patterns on the number grid and the worksheet, was initially presented to the class by a substitute teacher. After the lesson, none of the students were able to complete the worksheet. Attributing the students' difficulties to the fact that there was a substitute in the room, one that they have had problems with in the past, we repeated the lesson the following day with similar results. While the students seemed to have a good grasp on the concepts while they were working on the rug, they could not translate those skills to the worksheet. It was at this point that I decided to modify the lesson, breaking it down into two separate lessons and adding the hands on practice of the human puzzles. I also added the two number grid games to help the students further practice the skills.
This is a math lesson plan and is intended for the third trimester of the first grade. As the skills are ones that the students have continually struggled with (particularly counting forwards and backwards by 10's on a number grid) it was presented to the whole class. The lesson is comprised of two whole group lessons, two worksheets to be completed individually and two games that can be played in small groups of two to four students. The lesson is also appropriate for smaller groups of students with no modifications necessary.
To differentiate the lesson, students are given the opportunity to explore the patterns on the number grid as a whole class, through worksheets and by playing games. They may use tools such as the number grid on their nametags or the poster at the front of the classroom. They may also request assistance from their peers in the form of clues and hints to help them determine answers to the human number puzzles. For this particular lesson there is no need to plan for diversity perspectives, as the students are all familiar with the tools being used (number grid, dice, etc.).
Number Grid Puzzles: Part I
Objectives: Fill in the missing numbers on a number grid using patterns and then solve the human number grid puzzles. Complete worksheet 9-3: Number Grid Pieces.
Key Concepts and Skills:
- Count forwards and backwards by 1's and 10's using a number grid (Number and Numeration Goal 1).
- Identify the value of digits in a two digit number (Number and Numeration Goal 3).
- Extend patterns on a number grid (Patterns, Functions and Algebra Goal 1).
- Solve number grid puzzles (Patterns, Functions and Algebra Goal 1).
Materials:
- Number Grid poster
- Sticky notes/slips of paper (to cover up numbers)
- Math flash cards, 4-6 cards grouped to represent a row or column on the grid
- Math Masters page 258 (pre cut into fourths)
- Folders or mini offices for privacy
- Overhead of Math Masters page 258 (optional)
The Lesson:
Have the students identify the patterns they see in the numbers, including:
- The numbers increase as you move down the grid.
- The numbers increase as you move to the right.
- The tens digit increases as you move down a column.
- The ones digit increases as you move to the right in a row.
- The ones digit stays the same in a column.
- The tens digit stays the same all the way across a row.
Next, ask the students to close their eyes. Remove or cover up a few numbers from the number grid. Ask the students to determine the missing numbers, describing the pattern they used (responses will vary, but will likely include "I counted up/back by ones/tens").
Once the students are comfortable with the concept take down the number grid poster and call up a group of four to six students to the front of the room. Have them stand in a way that represents a column or a row in the number grid. Hand one or two students a math flash card and ask the remaining students in the group to determine what number they should be holding. They can ask their peers for clues such as "Count up by 10's" but not for the answers. Depending on the students skill level you can give them an answer key, a small group of numbers to choose from. Conversely, you can have the students hold up the unidentified numbers so they cannot be seen and have their peers on the rug identify the missing numbers. Figure 1.1 is a representation of what this may look like.
Figure 1.1: The students must use the patterns on the number grid to determine that the missing numbers are 12, 14, 15 and 17 respectively.
For today, stick to rows and columns of numbers, so that the students are only looking at one pattern at a time. Repeat with different numbers until all of the students have had a turn.
Figure 1.2: ¼ of worksheet 9-3: Number Grid Pieces (adapted from Everyday Math).
Have the students return to their seats and pass out worksheet 9-3. Tell the students that this must be completed individually (you can use folders or mini offices to separate them in necessary and that they may use the number grid on their nametag. Students who wish to try it without the number grid can flip their nametag over or push it off to the side. Once all of the students have completed the worksheet go over it as a class. Have the students put aside their pencils and use crayon to correct any mistakes. Draw a copy of the worksheet on the board or use an overhead sheet and call on students to come up and fill in the missing numbers. Have them describe what pattern they used to determine the answer. You can collect the correct worksheets for your own records or make notes about the students successes and difficulties as the lesson progresses.
Conclusion:
After the initial lesson, presented by the substitute, the students could not complete worksheet 9-3 individually, nor could they do it with a new set of numbers after hearing the lesson a second time. After completing the hands on activity the students were presented with the worksheet a third time with yet another set of numbers. This time the whole class was able to complete the worksheet and several of the students did so without usingthe number grids on their nametags.
Number Grid Puzzles: Part II
Objectives: Fill in the missing numbers on a number grid using patterns and then solve the human number grid puzzles. Complete worksheet 9-3: Number-Grid Puzzles, found on page 180 of Math Journal 2. Practice working with patterns on the number grid by playing Number Grid Shapes using Activity Sheets 15 and 16 from Math Journal 2 and by playing the Number Grid Game.
Key Concepts and Skills:
- Count forwards and backwards by 1's and 10's using a number grid (Number and Numeration Goal 1).
- Identify the value of digits in a two digit number (Number and Numeration Goal 3).
- Extend patterns on a number grid (Patterns, Functions and Algebra Goal 1).
- Solve number grid puzzles (Patterns, Functions and Algebra Goal 1).
Materials:
- Number Grid poster
- Sticky notes/slips of paper (to cover up numbers)
- Math flash cards, 4-6 cards grouped to represent a small chunk of the grid
- Math Journal 2, page 180 and Activity Sheets 15-16
- Dice and small playing pieces for the Number Grid Game
- Scissors
- Home Link 9-2
The Lesson:
Assemble the students on the rug and remind them of the patterns they discussed in the previous lesson, Number Grid Puzzles: Part I. Ask the students to name the patterns they observed. Tell the students that today they are going to work with those same patterns and ask them to closer their eyes. Remove or cover up a small chunk of numbers on the number grid poster. Refer to Figure 2.1 for suggestions.
Figure 2.1: Suggested shapes for covering up numbers on the number grid (adapted from Everyday Math)
Call on the students to fill in the missing numbers, asking them to explain how they found their answers. Students may find this more difficult than they did in part I, as it requires them to look at more than one pattern at a time. If necessary, demonstrate to the class how you would solve the problem.
Once the students have mastered working with the patterns on the number grid, have them repeat the human number grid puzzles, again using small chunks from the number grid instead of only columns and rows. Be sure to cover up the number grid poster to ensure that the students are using the patterns and not just looking at the poster.
Call up a group of four to six students to the front of the room and arrange them in the appropriate pattern. Hand one or two students a math flash card and ask the remaining students in the group to determine what number they should be holding. They can ask their peers for clues such as "Count up by 10's" but not for the answers. Depending on the students skill level you can give them an answer key, a small group of numbers to choose from. Conversely, you can have the students hold up the unidentified numbers so they cannot be seen and have their peers on the rug identify the missing numbers. Figure 2.2 is an example of what this may look like. Repeat using different sections of the number grid until all of the students have had a turn.
Figure 2.2: The students must use the patterns to determine that the missing numbers are 42, 43, 53 and 55, respectively.
After completing the whole group lesson have the students play the Number Shapes Game and the Number Grid Game and complete page 180 in Math Journal 2 (this can be a teacher directed activity).
Number Shapes Game:
Refer to figures 2.3 and 2.4 for Activity Sheets 15 and 16
This game is similar to the whole group activity done at the beginning of the lesson using the number grid. Students can work in pairs or in teams of two. The students must first cut out the number grid shapes on ActivitySheet 16. To play one student, or team of students, will cover their eyes or turn away while their partner covers up a section of the number grid using one of the number grid shapes. The first student, or team, must determine the missing numbers. Once they have figured out what numbers are missing the students will switch roles. The second student will cover their eyes while the first student covers up a portion of the number grid. Student can play for the entirety of the period or there can be a set time limit.
Number Grid Game:
Refer to Figure 2.3 for Activity Sheet 15 and Figure 2.5 for a copy of the rules. Students will also require one die and two playing pieces. Students can play in pairs or as teams of two.
To play each student places their token on the 0 on the number grid (Activity Sheet 15). The first student will role the die. How far they can more their token is determined by the number they role. Figure 2.6 shows what each face of the die represents.
Figure 2.6: The Number Grid Game movement table (adapted from Everyday Math).
Students may only move forward 10 or 20 spaces if there is enough room on the number grid to do so. If not they must move their token only 1 or 2 spaces. For example, if Player 1 has his token on 91 and proceeds to roll a 2 he must move forward 2 spaces, not 20.
The students will continue to take turns rolling the die and moving their token that many spaces on the number grid. The first player to land on 110 with an exact roll is the winner.
The game can also be played with the game starting on 110 and the students working backwards to 0, using the same rules.
Math Journal 2: Page 180
Refer to Figure 2.7 for worksheet 9-3: Number Grid Puzzles 1.
Inform the students that the worksheet is set up like the number grid and has spaces for the numbers 0-110. They need to fill in the missing boxes outlined in bold, using the patterns they have been working with for the last two days. Students can use the number grids on their nametags to check their work but they need to be able to discuss the patterns with a teacher if asked.
Homework:
Students will take home and complete Home Link 9-3 (Figure 2.8). They need to show someone at home how to solve the number grid puzzles, explaining to this person about the patterns they have observed on the number grid. The homework will be discussed the following day during Morning Math.
Conclusion:
When the students first attempted page 180 in Math Journal 2 they struggled with it. Figure 2.9 shows a student's initial efforts on the worksheet. The circled boxes represent areas where the student had difficulty and needed teacher assistance to correctly fill in the boxes. After the supplemental practice of the human number puzzles and the Number Grid games students were able to complete page 180 much more easily, as evidenced by Figure 2.10. This student was able to complete the worksheet without any assistance. Math Journal page 180 will be retained for remainder of the school year as a record of how well the student comprehended the lesson. Any additional help the student receives on this concept will be determined by this as well as observations made while the student played the two number grid games. The students will be further assessed on this concept, as well as the other concepts discussed in unit 9 in the Final Unit Assessment provided by Everyday Math.
Figure 2.3: Number Grid Worksheet for the Number Shapes Game and the Number Grid Game (adapted from Everday Math)
Figure 2.4: Shapes for the Number Shapes Game. These shapes have been cut and pasted from the original Activity Sheet 16 (Everyday Math) for the purpose of this paper.
Figure 2.5: The rules for the Number Grid Game (adapted from Everyday Math).
Figure 2.7: Math Journal 2, page 180: Number Grid Puzzles 1 (adapted from Everyday Math).
Figure 2.8: Number Grid Puzzles 1, completed by a student prior to participating in the revised Number Grid Puzzles lesson. Circled sections indicate where the student was initially incorrect (worksheet from Everyday Math).
Figure 2.9: Number Grid Puzzles 1, completed by a student after participating in the revised Number Grid Puzzles lesson. This student was able to complete the worksheet without any additional assisstance (worksheet from Everyday Math).
Figure 2.10: Homework corresponding to the Number Grid Puzzles lesson (adapted from Everyday Math).
References
Everyday Mathematics.