# How Did You Solve the Puzzle?

This lesson can be used as a pre-lesson for the Solving KenKen PuzzlesLesson plan.

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This lesson can be used as a pre-lesson for the Solving KenKen PuzzlesLesson plan.

Students will be able to apply logic and their knowledge of addition, subtraction, multiplication, and division to solve grid puzzles.

##### Language

Students will be able to explain and compare strategies used to solve grid puzzles using sentence starters.

(6 minutes)
• Show students a copy of a blank Frayer model. Write the word PuzzleIn the middle and model to students how you complete it.
• Define the term "puzzle" (something that needs to be solved), draw an image to match, write an example and non-example.
• Ask students to turn and talk to a partner about their experiences with puzzles (jigsaw puzzles, crossword puzzles, etc.).
• Have students share out their experiences with the whole class.
• Explain that today they will learn how to Solve, or find the answer to, a certain type of puzzle called a GridPuzzle. Show students the vocabulary cards for the remaining tiered words and have a few students orally share a sentence using each vocabulary word.
(8 minutes)
• Read aloud the content and language objectives for the lesson and ask students to repeat them.
• Show examples of grid puzzles such as the KenKen puzzle and the Four Addition Puzzle worksheets. Have students share their observations of the puzzles by using the sentence stems: "I notice... This grid puzzle is/has..."
• Explain that there are many types of grid puzzles to solve and that they are all helpful in getting us to use logic and explain our maths reasoning. Tell students that people solve puzzles in different ways or using different strategies, and that no one strategy is better than another as long as the puzzle is solved correctly.
• Inform them that today they will learn how to practise one type of addition grid puzzle and compare their strategy to that of their partner.
• Display the directions from the Addition maths Puzzles #3 worksheet and review them with students. Emphasize that each puzzle contains the numbers 5–13 and that no numbers can repeat. The numbers on the outside of the box represent the Sum, or answer to an addition problem, of the three numbers in that row or column. Label the terms "row" and "column" to make sure students understand the meaning of the words.
• Take the first example of the grid puzzle (upper left) from the Addition maths Puzzles #3 worksheet and model aloud how to solve it, pointing to each part of the puzzle as you work on it.
• Write down each step and explain your reasoning as you go (e.g., "First I look for a row or column that has two numbers. I see a 6 and an 8. The sum outside of the grid is 26. Then, I can build a maths expression of 6 + 8 + ? = 26. I add 6 to 8 and get 14. I have to think of a number to add to 14 to get to 26. I will subtract 14 from 26 to get 12. Therefore, I know that the missing number is 12.").
• Continue solving this grid puzzle until all the numbers have been solved. Show students how to double check to make sure that all the rules of the puzzle were followed.
(8 minutes)
• Create a chart paper with sentence starters for students as a reference to help them describe their maths reasoning. For example:
• "First, I look for..."
• "Then, I find the sum of..."
• "The sum in that row/column is ____Which means that..."
• "I have to find the sum of ____And ____, and subtract the sum from ____."
• "I made a mistake here when I..."
• "I know my puzzle is correct because..."
• Place students into partnerships. Hand out one grid puzzle to each pair of students from the Addition maths Puzzles #3 worksheet. (Note: make sure that 2 pairs of students have the same grid puzzle so that they can compare their processes later). Then instruct them to place it on the desk in between them.
• Give them each a piece of scratch paper and have them work on the puzzle together with their partner. Tell each student to write down the steps they took to solve for each number on their scratch paper and explain their thinking, using the sentence starters displayed.
• Invite a couple pairs of students to share their completed grid puzzle with the whole group, describing their process and reasoning.
(8 minutes)
• Place two pairs of students that worked on the same grid puzzle into a group of four. Have them orally discuss the strategies used to solve the puzzle.
• Provide the following questions and sentence frames/stems as a guide to stimulate students' conversations:
• What was your strategy to solve the grid puzzle? ("Our strategy was to...")
• What is a difference or similarity between your strategy and ours? ("A difference is that you... while we..." Or"A similarity between the two strategies is that they both...")
• Which box did you solve first and why? ("We solved for the ____First because...")
• Did it get easier or harder to figure out the number as you went along and why? ("It got easier/harder to figure out the number as we went along because...")
• Is there anything you would do differently the next time you solve a grid puzzle? ("Next time, I would...")
• Listen in on students' group conversations and take notes on a piece of chart paper. Write down the name of each student that spoke next to the quotes you record.
• Direct students' attention to the chart paper, and read aloud each comment you recorded as you state who said it (e.g., "Joanna said that she and her partner used the strategy of counting up to the sum to figure out the missing number.").
• Draw some conclusions from the documentation of students' conversations. Ask students to reflect further on how their strategies and methods differ from each other. Model this first (e.g., "I notice that Adam and Markel chose the strategy of solving the rows before they double checked their answers by focusing on the columns, while Gia and Axel didn't focus on any particular order.").
• Validate all students' strategies and emphasize the wealth of information that you gathered about students' mathematical thinking and processes simply by listening to their discussions.

Beginning

• Give students access to bilingual glossaries and online dictionaries for them to look up unfamiliar words throughout the lesson.
• Place students with more advanced ELs for partner work.
• Pull aside a small group of students as they work on the puzzle and guide them through the process.
• Have students repeat the directions in their home language (L1) or in English (L2) before beginning the work.
• Allow students to work on the formative assessment piece with a helpful partner.

• Encourage students to speak and write their answers without using the sentence frames/stems.
• Allow students to be the first to share their ideas or rephrase their classmates' contributions to class discussions.
• Haves students create and display a word/phrase bank with helpful terms from the lesson for reference purposes, with images if applicable.
(7 minutes)
• Hand out an individual grid puzzle from the Addition maths Puzzles #7 worksheet. Have students complete the puzzle independently.
• Place students with a new partner and have them check each other's work on the grid puzzle. Tell students to refer to the displayed questions and sentences starters to help them talk about the puzzles.
(3 minutes)
• Have students volunteer to share their experiences of completing grid puzzles, using this sentence starter: "I liked/disliked solving grid puzzles because..."
• Remind students that they are likely to see more types of grid puzzles in the future. It is valuable for them to learn the skills of following a set of rules to solve grid puzzles not only because it helps them with their maths skills and reasoning, but also because they are fun and satisfying to do.

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