- My students really benefited from all of the problems asking them to analyze and compare solutions. They seemed to enjoy digging into the fake students’ work: They reasoned, made connections, and learned from these examples. I will never skip problems like these again. It’s a highly effective way to push kids to make sense of more advanced algebraic reasoning.<\/li><\/ol>\n\n\n\n
An example from Lesson 3<\/a>:<\/p>\n\n\n\n
![\"\"](\"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/Screen-Shot-2022-04-11-at-2.29.01-PM.png?resize=723%2C228&ssl=1\")
2. For some kids the leap from the hanger diagrams to solving complex equations was too quick. Here are a few of the ways we differentiated:<\/figcaption><\/figure>\n\n\n\n - Lesson 5: Small group for kids who needed more time to make sense of how apply their reasoning about hanger diagrams to reasoning about equations. <\/a> (This set them up well for Lesson 6 because which offers them the choice to continue working on simpler equations.)<\/li>
- Lesson 8: Created a second version of the card sort<\/a> that includes some balance diagrams and simpler equations with friendlier numbers<\/li><\/ul>\n\n\n\n
![\"\"](\"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/IMG_20220418_1309528283-1.jpg?resize=723%2C297&ssl=1\")
<\/figure>\n\n\n\n3. Kids did seem to need more practice to build fluency than IM offers, but maybe that’s because we’re still in a pandemic and absences were wild during the omicron surge. In any case, we added in a day of “Building Thinking Classroom” thin-slicing practice and a day of “Sage and Scribe” practice where partners could choose equations with different levels of difficulty.<\/p>\n\n\n\n
4. At the end of lesson 6, I asked students to share their tips for solving equations. This led to a fantastic anchor chart that supported everyone throughout the rest of the unit. This was SO much better than the direct instruction I used to do, but still made the main skills explicit. <\/p>\n\n\n\n
\n<\/div>\n<\/div>\n\n\n\n\n\n![\"\"](\"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/IMG_20220418_1310026146-1.jpg?resize=384%2C434&ssl=1\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/IMG_20220418_1310116243.jpg?resize=294%2C305&ssl=1\")
<\/figure>\n<\/div>\n\n\n\n\n![\"\"](\"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/IMG_20220418_1310026147.jpg?resize=384%2C488&ssl=1\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/IMG_20220418_1310026145.jpg?resize=384%2C214&ssl=1\")
<\/figure>\n<\/div>\n<\/div>\n\n\n\nLingering questions:<\/strong> <\/p>\n\n\n\n
By the end of the unit, most kids still couldn’t consistently solve many of the equations with fractions. They have so much unfinished learning around fractions and I just haven’t been successful at weaving it into 8th grade math in a way that sticks or builds proficiency. What should I try next?<\/p>\n\n\n\n
<\/p>\n\n\n\n
<\/p>\n\n\n\n
<\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
I believe in a problem-based approach to learning math (I brought IM to my school, damnit!), but for some reason whenever Unit 4: Linear Equations and Systems of Equations rolled around, I felt the need to deviate from IM’s curriculum. I couldn’t quite envision how it would work: the equations seemed to get too complicated […]<\/p>\n","protected":false},"author":1,"featured_media":1372,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"Reflections on Unit 4 Illustrative Mathematics and Open Up Resources. Modified and differentiated Unit 4. Anchor charts too.","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[4,5,10,1],"tags":[15,41,79,53,72],"class_list":["post-1314","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8th-grade-math","category-algebra","category-open-up-resources-illustrative-mathematics","category-uncategorized","tag-mtbos","tag-illustrative-mathematics","tag-open-up-resources","tag-open-up-resources-illustrative-mathematics","tag-solving-equations"],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/hailstonesequence.com\/wp-content\/uploads\/2022\/04\/IMG_20220418_1310026146.jpg?fit=964%2C1090&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts\/1314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/comments?post=1314"}],"version-history":[{"count":3,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts\/1314\/revisions"}],"predecessor-version":[{"id":1379,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/posts\/1314\/revisions\/1379"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/media\/1372"}],"wp:attachment":[{"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/media?parent=1314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/categories?post=1314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hailstonesequence.com\/index.php\/wp-json\/wp\/v2\/tags?post=1314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Lesson 8: Created a second version of the card sort<\/a> that includes some balance diagrams and simpler equations with friendlier numbers<\/li><\/ul>\n\n\n\n
- Lesson 5: Small group for kids who needed more time to make sense of how apply their reasoning about hanger diagrams to reasoning about equations. <\/a> (This set them up well for Lesson 6 because which offers them the choice to continue working on simpler equations.)<\/li>