This algorithm works well for students who are developing multiplication fact fluency. Students may begin using a template to solve multiplication problems, but they quickly learn to draw their own lattice matrix to solve problems. Students love the method and it is very successful with both whole numbers and decimals. Teach students this multiplication algorithm as one of many different algorithms they may elect to use. Students will very quickly learn to multiply large numbers, using basic multiplication facts and addition/regrouping skills.
Procedure:
Student writes the problem in the grid (e.g. 6 x 417).
Student then writes the answer to each single digit multiplication in the appropriate square.
The tens digit is placed above the diagonal; the ones digit below the diagonal.
When all squares have been completed, the student sums the numbers between each set of diagonals, and writes the sum at the bottom of the grid. NOTE: If the sum is greater than 10, regroup the ten to the next diagonal to the left.
The student can now simply read the answer from left to right and insert commas, as appropriate.
For a complete overview of this method, see Cool Math's explanation of Lattice Multiplication to view the step-by-step procedure. Take a cue from the site's explanation and use colored markers when introducing this algorithm to students on the overhead or whiteboard.
Templates: Three different templates are included for Lattice Multiplications. Templates are designed to be used in sheet protectors. This strategy allows students to use dry-erase markers and re-use the same paper for many multiplication problems.
Download the Lattice grids for a single digit multiplier.
Download the Lattice grid for a 2-digit multiplier.
Download the Lattice grid for 2-3 digit multipliers.
Students insert the template into a sheet protector and use dry erase markers to reproduce the domino, then add in the appropriate numbers. Finally students, write four number sentences for that fact family.
This activity is easily incorporated into daily lessons as a warm-up or do now! activity. Teachers may post the domino of the day or use an overhead domino. Teachers may also elect to distribute dominoes, differentiating the difficulty level to accommodate the needs of varied learners in the class.
This activity is also an effective math center activity. Provide tubs of dominoes, domino facts templates and/or have students use the Domino Record Sheet to record the sums of dominoes they select to practice basic facts.
Changes in temperature are a real-life application of integers in mathematics. 3 degrees warmer would be represented as +3 while 5 degrees colder would be represented as a change of -5. This change in temperature use of positive and negative integers is in addition to the absolute temperatures on a thermometer which might read below 0 in some climates.
Students use this template to record data to solve changes in temperature problems. Using the 5-day forecast, the teacher tells students Monday's temperature and the change (+ or -) for each day of the week. Students use this information to figure out the actual temperature for each day of the week. Note that the change should reflect the change from the previous day. For example, a change of -3 for Wednesday means that the temperature went down 3 degrees from Tuesday's temperature. Additionally, if the teacher uses the actual changes in the 5-day forecast for the area, the students can also assess the accuracy of a 5-day forecast as the week's weather plays out.
Place the template in a clear sheet protector and provide dry erase markers for students to use.
The thermometer strip is available as a visual representation for students to use in solving the changes in temperature problems. Students write Monday's temperature in the START space. They may then simply count up or down spaces to get to the next day's temperature.
The template was designed so that students could use a clothespin to mark the daily change for ease in recording on the template pictured above. The clothespin simply clips onto the appropriate space as a placeholder while students write in the temperature and record the information in the weekly chart.
Download the Changes in Temperature Template which also includes thermometer strips that may be laminated for student use in these lessons.
This function machine game was created to give students practice in saying and writing the rule, given an input/output table. One student has the rule which the other student has to guess. The guesser records an input number in the table. The rule person must apply the rule and tell the output number. Student pairs repeat this until the guesser correctly identifies the rule by saying and writing it. Students then switch places and repeat the activity.
Download three different levels of rules for play: simple addition & subtraction, multiplication or two-step rules.
Download a function machine template designed to be inserted into a clear sheet protector and used with dry erase markers for easy game play.
Differentiation: This game is easily differentiated by varying the rule cards provided to students. Use simple one-step addition and/or subtraction for basic skills students and challenge better students by graduating them to 2-step rules. Consider printing the different level rules on different color paper so that students may easily select the proper level from the math center.
Enrichment: Provide blank cards for students to create their own rules to challenge their peers. Be sure that students try their rule on at least 3 other students to be sure that they have written it correctly.
This game challenges students to find equivalent names for numbers. In Tribuation, students must search the gameboard for 3 numbers in a row (vertically, horizontally or diagonally as in a word search) that combine to make the target number. In this game, however, there is a prescribed formula for combining the numbers. Students must multiply the first two numbers then add or subtract the third number to produce the target number
Students quickly learn that any string of three numbers produce four different results since the string of numbers can be considered both forwards and backwards as in word searches. Consider that the numbers 3, 5 and 8 are in a horizontal row. These three numbers produce the following results when combined in the formula:
3 x 5 + 8 = 23
3 x 5 - 8 = 7
8 x 5 + 3 = 43
8 x 5 - 3 = 37
Note that the student may not begin with the middle number. Once again, students will perform many mental calculations in a search for a viable solution on the gameboard.
This game was originally a board game in the 1980s but has been developed into a classroom game using a gameboard template designed to be inserted in a sheet protector and used with dry-erase pens so that students can easily circle and record solutions. Two different approaches are effective in using this game: (1) students search for one solution for 6-8 different target numbers, and (2) students search for many different solutions for one number. Samples of both types of activities are included in the Tribulation directions packet for teachers.
Read more about the Tribulation Game on Mathwire.com to download instructions and templates that can be inserted in sheet protectors for daily use.
Encourage active participation in class by using whiteboards and templates. Both tools should be regulars in classroom lessons and each student must be required to participate in these mini-assessment activities.
Teachers who effectively incorporate whiteboard and/or template activities gather useful data about which students understand or are proficient, which students need some additional guided practice or instruction and which students are missing some of the prerequisite skills for the particular lesson or need a different approach to the concept or skill.
Be sure to check out these Mathwire collections for ideas on incorporating white boards and templates in math lessons:
Try out these strategies and begin replacing some oral classroom questioning with questions and/or problems that require each student to write down answers on whiteboards or math templates. These mini-assessments require students to stay on-task and and holds each student accountable for explaining math concepts in words, pictures, and numbers. Plus, students get to see how their peers explain a term or picture a mathematical problem which adds to their own problem-solving repertoire.
